From Breffni O'Rourke — David Alexander and Phil Stewart, "Nine officers removed, one resigns in Air Force cheating probe", Reuters 3/27/2014:
Nuclear critics say the problem is deeply rooted and has been going on for years, becoming increasingly acute since the end of the Cold War as the nuclear mission has increasingly come to be seen as a dead-end career that's relevance is in decline.
Breffni comments "I don't think I've come across that before. Maybe the writer was trying to avoid 'whose' with a non-human head?"
The possessive form of that-the-complementizer seems wrong to me, presumably for the same reason that "that" doesn't work in e.g. "a career the relevance of which/*that is in decline", or "… the prison from which/*that they escaped".
But this is certainly not the first time someone has been inspired to take possessive-complementizer that out for a spin, on the theory that it's really a kind of pronoun. For instance, there's an exchange on Yahoo! Answers starting with this question:
Hi! So I'm writing a paper and I'm saying, "Darfur is a region of western Sudan thats government is…" My question is about the "that"– should it be "that's" (even though that means "that is") or "thats" (with no apostrophe)? My computer says it should be "that's", but I need a serious, concrete answer for the correct grammar. Thank you!
It's not easy to find other examples, since the -'s in that's is usually a contracted form of is rather than the possessive. But maybe there are English varieties where things work differently?
Update — I spent the afternoon in an interesting panel discussion at PLC 38, and it's a real pleasure to come back and read such a marvelous collection of thoughtful and informative comments.