There's no official term for this. I also think of it as "progressed improper".
Rick Mohr's written a number of dances like this -- for instance: Leave the Wine, My Marbles Have Many Moods, Synchronicity. These are all dances that can start proper, but after the first time default to progressed improper. (Another curiosity that starts improper and then converts to other formations is "People of the Pond" by Jim Saxe.) It's an interesting choice (all of Rick Mohr's dances could be Becketed), but I don't see problems on the dance floor when they're done, as long as dancers are reassured it's not a bug. More and more, I think not about what formation the dance is in, but what formation the dancers progress with -- whether they progress/get back into the dance improper, indecent, becket, or something else. -Chris Page San Diego p.s. The square through dance from an earlier post is a probably mistranscribed version of "Stir Crazy" by Erik Weberg. The original is Becket.
