Mm, I think it could come up quite naturally as "she must have been being watched" in something like:
Two detectives are watching security film.
DETECTIVE 1
And then from 9:07 to 9:14 she started acting very cautiously, but –
Detective 1 rewinds the tape by a few seconds and gestures at the screen.
DETECTIVE 1
– from this angle you can tell that she's making an effort to not seem suspicious. I wonder why?
DETECTIVE 2
She must've been being watched.
I do agree that form "must have had been being —ed" (with "had" in there as well) is an especially rare form, but in context, native English speakers understand what it means!
I wonder how many other constructions there are that native speakers don't really produce but that they still consider grammatical or as not even being unusual.
I wonder how many other constructions there are that native speakers don't really produce but that they still consider grammatical or as not even being unusual.