When I run emacs with -Q, I'm unable to produce the problem! (It's not multishell, per se - I'm unable to produce it via multishell or separately from it, in an emacs started with -Q.) I'll remove the notes in multishell about it, and work on isolating what in my local setup is at fault.
Interestingly, the problem does happen if I start emacs with '-q', instead of '-Q' (I didn't even think about trying -Q until you suggested it). This suggests that the problem is in something my my site configuration, I gather. I'll try to uncover it, but it looks like that's going to be via a process of elimination. Unfortunately, I don't get a traceback, even with tramp-verbose=6, when the problem occurs, only "Selecting deleted buffer", and in *Messages*, "byte-code: Selecting deleted buffer". Nothing more happens if debug-on-error and debug-on-signal are set. This all suggests to me that something is swallowing the signal, yet still returning to top-level. I'd be interested to hear if there's common strategies for dealing with such a puzzle.
Thanks for following up, and steering me in the right direction. Sorry about misleading anyone, mistaking the problem as being in tramp rather than some combination. I'll let you know if there's anything interesting about what's actually responsible for the problem, when I uncover it, and suggestions about investigating the "Selecting deleted buffer" thing would be appreciated.