This is indeed an interesting and uncommon subject. I've had a few 244s and seen countless in the yards without ever seeing something like what you describe. Even had one to be totally inundated -- a sunroof car at that -- and in the months it took me to pull what wasn't ruined, saw no unusual change to the headliner.

The factory body repair (TP30303/3) shows a procedure to replace the headliner in a 4-door sedan. For the years up to 79 it says the rear window must be removed, but 1980 and beyond (Manual published 1986) it says to remove the complete rear seat to obtain access to the C-pillar side panels. And to disconnect the heated rear window. Only for the 2-door (242) does it show bringing the panel in through the open front door.
--
Art Benstein near Baltimore

"The one thing that I love on a long trip is the occasional smell of diesel. It is one odor I know doesn't get produced by my car."