+1... Bottom line is the cats have to go, or you're gonna be living in a van down by the river, eating a steady diet of government cheese. Sounds like Mom and Dad are shell shocked by the situation they're presently in, and are unable to deal with it realistically. Denial and depression have to be part of the problem, that's understandable.
Counseling and/or medication might be needed to help get them moving towards resolving this dilema. Good luck.