Ned Batchelder added the comment:

I doubt very very much that coverage.py is stealing stderr.  Many many test 
suites would have this problem if that were true.  More likely is that somehow 
__del__ is not being invoked when you need it to be.

I tried running the tests under coverage also, and did not see this behavior. I 
don't have a build tree of the latest code, but I ran it on 3.6.0.  The tests 
passed both with and without coverage measurement (output below).  I would like 
to understand why you are seeing the results you are.

$ mkvirtualenv -p python3.6 issue29048
Running virtualenv with interpreter /usr/local/bin/python3.6
Using base prefix '/usr/local/pythonz/pythons/CPython-3.6.0'
New python executable in issue29048/bin/python3.6
Also creating executable in issue29048/bin/python
Installing setuptools, pip, wheel...done.
Collecting pip
  Using cached pip-9.0.1-py2.py3-none-any.whl
Collecting setuptools
  Using cached setuptools-32.2.0-py2.py3-none-any.whl
Installing collected packages: pip, setuptools
  Found existing installation: pip 7.1.2
    Uninstalling pip-7.1.2:
      Successfully uninstalled pip-7.1.2
  Found existing installation: setuptools 18.2
    Uninstalling setuptools-18.2:
      Successfully uninstalled setuptools-18.2
Successfully installed pip-9.0.1 setuptools-32.2.0
(issue29048)$ pip install coverage
Collecting coverage
Installing collected packages: coverage
Successfully installed coverage-4.2
(issue29048)$ python3.6 -m test -v test_exceptions
== CPython 3.6.0 (default, Dec 23 2016, 07:11:25) [GCC 4.2.1 Compatible Apple 
LLVM 7.0.2 (clang-700.1.81)]
==   Darwin-14.5.0-x86_64-i386-64bit little-endian
==   hash algorithm: siphash24 64bit
==  cwd: 
/private/var/folders/j2/gr3cj3jn63s5q8g3bjvw57hm0000gp/T/test_python_20266
==  encodings: locale=UTF-8, FS=utf-8
Testing with flags: sys.flags(debug=0, inspect=0, interactive=0, optimize=0, 
dont_write_bytecode=0, no_user_site=0, no_site=0, ignore_environment=0, 
verbose=0, bytes_warning=0, quiet=0, hash_randomization=1, isolated=0)
Run tests sequentially
0:00:00 [1/1] test_exceptions
testAttributes (test.test_exceptions.ExceptionTests) ... ok
testChainingAttrs (test.test_exceptions.ExceptionTests) ... ok
testChainingDescriptors (test.test_exceptions.ExceptionTests) ... ok
testExceptionCleanupNames (test.test_exceptions.ExceptionTests) ... ok
testExceptionCleanupState (test.test_exceptions.ExceptionTests) ... ok
testInfiniteRecursion (test.test_exceptions.ExceptionTests) ... ok
testInvalidAttrs (test.test_exceptions.ExceptionTests) ... ok
testInvalidTraceback (test.test_exceptions.ExceptionTests) ... ok
testKeywordArgs (test.test_exceptions.ExceptionTests) ... ok
testNoneClearsTracebackAttr (test.test_exceptions.ExceptionTests) ... ok
testRaising (test.test_exceptions.ExceptionTests) ... ok
testSettingException (test.test_exceptions.ExceptionTests) ... ok
testSyntaxErrorMessage (test.test_exceptions.ExceptionTests) ... ok
testSyntaxErrorOffset (test.test_exceptions.ExceptionTests) ... ok
testWithTraceback (test.test_exceptions.ExceptionTests) ... ok
test_3114 (test.test_exceptions.ExceptionTests) ... ok
test_MemoryError (test.test_exceptions.ExceptionTests) ... ok
test_WindowsError (test.test_exceptions.ExceptionTests) ... ok
test_badisinstance (test.test_exceptions.ExceptionTests) ... ok
test_errno_ENOTDIR (test.test_exceptions.ExceptionTests) ... ok
test_exception_target_in_nested_scope (test.test_exceptions.ExceptionTests) ... 
ok
test_exception_with_doc (test.test_exceptions.ExceptionTests) ... ok
test_generator_close_cleanup_exc_state (test.test_exceptions.ExceptionTests) 
... ok
test_generator_del_cleanup_exc_state (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_doesnt_retain_old_exc (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_finalizing_and_exc_info (test.test_exceptions.ExceptionTests) 
... ok
test_generator_leaking (test.test_exceptions.ExceptionTests) ... ok
test_generator_leaking2 (test.test_exceptions.ExceptionTests) ... ok
test_generator_leaking3 (test.test_exceptions.ExceptionTests) ... ok
test_generator_leaking4 (test.test_exceptions.ExceptionTests) ... ok
test_generator_next_cleanup_exc_state (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_send_cleanup_exc_state (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_throw_cleanup_exc_state (test.test_exceptions.ExceptionTests) 
... ok
test_memory_error_cleanup (test.test_exceptions.ExceptionTests) ... ok
test_recursion_error_cleanup (test.test_exceptions.ExceptionTests) ... ok
test_str (test.test_exceptions.ExceptionTests) ... ok
test_unhandled (test.test_exceptions.ExceptionTests) ... ok
test_unicode_change_attributes (test.test_exceptions.ExceptionTests) ... ok
test_unicode_errors_no_object (test.test_exceptions.ExceptionTests) ... ok
test_unraisable (test.test_exceptions.ExceptionTests) ... ok
test_windows_message (test.test_exceptions.ExceptionTests)
Should fill in unknown error code in Windows error message ... skipped 'test 
specific to Windows'
test_attributes (test.test_exceptions.ImportErrorTests) ... ok
test_non_str_argument (test.test_exceptions.ImportErrorTests) ... ok

----------------------------------------------------------------------
Ran 43 tests in 0.027s

OK (skipped=1)
1 test OK.

Total duration: 64 ms
Tests result: SUCCESS
(issue29048)$ python -m coverage run --pylib -m test -v test_exceptions
== CPython 3.6.0 (default, Dec 23 2016, 07:11:25) [GCC 4.2.1 Compatible Apple 
LLVM 7.0.2 (clang-700.1.81)]
==   Darwin-14.5.0-x86_64-i386-64bit little-endian
==   hash algorithm: siphash24 64bit
==  cwd: 
/private/var/folders/j2/gr3cj3jn63s5q8g3bjvw57hm0000gp/T/test_python_20270
==  encodings: locale=UTF-8, FS=utf-8
Testing with flags: sys.flags(debug=0, inspect=0, interactive=0, optimize=0, 
dont_write_bytecode=0, no_user_site=0, no_site=0, ignore_environment=0, 
verbose=0, bytes_warning=0, quiet=0, hash_randomization=1, isolated=0)
Run tests sequentially
0:00:00 [1/1] test_exceptions
testAttributes (test.test_exceptions.ExceptionTests) ... ok
testChainingAttrs (test.test_exceptions.ExceptionTests) ... ok
testChainingDescriptors (test.test_exceptions.ExceptionTests) ... ok
testExceptionCleanupNames (test.test_exceptions.ExceptionTests) ... ok
testExceptionCleanupState (test.test_exceptions.ExceptionTests) ... ok
testInfiniteRecursion (test.test_exceptions.ExceptionTests) ... ok
testInvalidAttrs (test.test_exceptions.ExceptionTests) ... ok
testInvalidTraceback (test.test_exceptions.ExceptionTests) ... ok
testKeywordArgs (test.test_exceptions.ExceptionTests) ... ok
testNoneClearsTracebackAttr (test.test_exceptions.ExceptionTests) ... ok
testRaising (test.test_exceptions.ExceptionTests) ... ok
testSettingException (test.test_exceptions.ExceptionTests) ... ok
testSyntaxErrorMessage (test.test_exceptions.ExceptionTests) ... ok
testSyntaxErrorOffset (test.test_exceptions.ExceptionTests) ... ok
testWithTraceback (test.test_exceptions.ExceptionTests) ... ok
test_3114 (test.test_exceptions.ExceptionTests) ... ok
test_MemoryError (test.test_exceptions.ExceptionTests) ... ok
test_WindowsError (test.test_exceptions.ExceptionTests) ... ok
test_badisinstance (test.test_exceptions.ExceptionTests) ... ok
test_errno_ENOTDIR (test.test_exceptions.ExceptionTests) ... ok
test_exception_target_in_nested_scope (test.test_exceptions.ExceptionTests) ... 
ok
test_exception_with_doc (test.test_exceptions.ExceptionTests) ... ok
test_generator_close_cleanup_exc_state (test.test_exceptions.ExceptionTests) 
... ok
test_generator_del_cleanup_exc_state (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_doesnt_retain_old_exc (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_finalizing_and_exc_info (test.test_exceptions.ExceptionTests) 
... ok
test_generator_leaking (test.test_exceptions.ExceptionTests) ... ok
test_generator_leaking2 (test.test_exceptions.ExceptionTests) ... ok
test_generator_leaking3 (test.test_exceptions.ExceptionTests) ... ok
test_generator_leaking4 (test.test_exceptions.ExceptionTests) ... ok
test_generator_next_cleanup_exc_state (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_send_cleanup_exc_state (test.test_exceptions.ExceptionTests) ... 
ok
test_generator_throw_cleanup_exc_state (test.test_exceptions.ExceptionTests) 
... ok
test_memory_error_cleanup (test.test_exceptions.ExceptionTests) ... ok
test_recursion_error_cleanup (test.test_exceptions.ExceptionTests) ... ok
test_str (test.test_exceptions.ExceptionTests) ... ok
test_unhandled (test.test_exceptions.ExceptionTests) ... ok
test_unicode_change_attributes (test.test_exceptions.ExceptionTests) ... ok
test_unicode_errors_no_object (test.test_exceptions.ExceptionTests) ... ok
test_unraisable (test.test_exceptions.ExceptionTests) ... ok
test_windows_message (test.test_exceptions.ExceptionTests)
Should fill in unknown error code in Windows error message ... skipped 'test 
specific to Windows'
test_attributes (test.test_exceptions.ImportErrorTests) ... ok
test_non_str_argument (test.test_exceptions.ImportErrorTests) ... ok

----------------------------------------------------------------------
Ran 43 tests in 0.036s

OK (skipped=1)
1 test OK.

Total duration: 95 ms
Tests result: SUCCESS
(issue29048)$ python -m coverage report
Name                                                                            
           Stmts   Miss  Cover
--------------------------------------------------------------------------------------------------------------
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/_bootlocale.py           
              17     13    24%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/_collections_abc.py      
             562    546     3%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/_osx_support.py          
             210    161    23%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/_sysconfigdata_m_darwin_darwin.py
       1      0   100%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/_weakrefset.py           
             146    109    25%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/abc.py                   
              92     65    29%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/argparse.py              
            1187    757    36%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/base64.py                
             315    268    15%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/codecs.py                
             398    377     5%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/collections/__init__.py  
             677    650     4%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/contextlib.py            
             163    140    14%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/difflib.py               
             669    606     9%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/email/__init__.py        
              14      8    43%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/email/base64mime.py      
              40     26    35%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/email/charset.py         
             122     78    36%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/email/encoders.py        
              28     19    32%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/email/errors.py          
              37      7    81%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/email/header.py          
             310    258    17%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/email/quoprimime.py      
             115     83    28%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/encodings/__init__.py    
              76     43    43%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/encodings/latin_1.py     
              19     18     5%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/enum.py                  
             438    248    43%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/functools.py             
             443    421     5%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/genericpath.py           
              72     50    31%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/gettext.py               
             389    323    17%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/gzip.py                  
             349    298    15%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/importlib/__init__.py    
              99     96     3%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/importlib/_bootstrap.py  
             631    445    29%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/importlib/_bootstrap_external.py
      711    528    26%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/importlib/util.py        
             147    140     5%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/ipaddress.py             
             904    597    34%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/linecache.py             
             102     55    46%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/locale.py                
             399    357    11%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/logging/__init__.py      
             769    521    32%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/logging/handlers.py      
             663    534    19%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/lzma.py                  
             135    130     4%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/multiprocessing/process.py
            163    162     1%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/nntplib.py               
             559    457    18%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/os.py                    
             536    489     9%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/platform.py              
             580    466    20%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/posixpath.py             
             320    222    31%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/pprint.py                
             419    351    16%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/queue.py                 
             111     76    32%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/quopri.py                
             168    150    11%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/random.py                
             346    329     5%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/re.py                    
             153    125    18%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/shutil.py                
             619    600     3%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/socket.py                
             403    396     2%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/sre_compile.py           
             401    151    62%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/sre_parse.py             
             758    460    39%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/ssl.py                   
             571    426    25%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/string.py                
             153    114    25%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/subprocess.py            
             794    671    15%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/sysconfig.py             
             376    246    35%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/tempfile.py              
             395    258    35%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/__init__.py         
               0      0   100%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/__main__.py         
               2      0   100%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/libregrtest/__init__.py
            3      0   100%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/libregrtest/cmdline.py
           127     52    59%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/libregrtest/main.py 
             335    163    51%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/libregrtest/refleak.py
           186    122    34%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/libregrtest/runtest.py
           146     62    58%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/libregrtest/save_env.py
          189     68    64%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/libregrtest/setup.py
              68     21    69%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/support/__init__.py 
            1289    902    30%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/test/test_exceptions.py  
             765     93    88%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/threading.py             
             575    572     1%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/tokenize.py              
             473    438     7%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/traceback.py             
             247    185    25%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/types.py                 
             155    152     2%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/__init__.py     
              15      3    80%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/case.py         
             753    413    45%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/loader.py       
             295    226    23%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/main.py         
             149    122    18%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/result.py       
             128     66    48%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/runner.py       
             159     51    68%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/signals.py      
              47     33    30%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/suite.py        
             220     81    63%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/unittest/util.py         
             130    107    18%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/urllib/__init__.py       
               0      0   100%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/urllib/error.py          
              34     19    44%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/urllib/response.py       
              43     26    40%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/warnings.py              
             331    300     9%
/usr/local/pythonz/pythons/CPython-3.6.0/lib/python3.6/weakref.py               
             379    342    10%
--------------------------------------------------------------------------------------------------------------
TOTAL                                                                           
           26517  19743    26%
(issue29048)$

----------

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