I'd like to know whether coding systems in general are supposed to be
    robust, meaning that decoding some random byte string into the coding
    system and reencoding it is guaranteed to deliver the same byte string
    again?

Handa is the expert, but I am sure this is not generally the case.  In
some coding systems there is more than one representation for the same
series of Emacs characters.  I think one of the coding system involves
shift-sequences that switch between sub-coding-systems.  Re-encoding
cannot preserve the shift-sequences.

There may be some coding systems that are 1-1 encodings for the
Emacs characters they can handle.


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