Did your parents foist your baby sister on you when they went out? It means they forced her on you. Anything — a person or object or idea — can be foisted if it's done by force upon an unwilling party.
Foist used to imply a degree of deception rather than just brute force, but that's a meaning that's pretty much lost now: if something's foisted upon you, you know about it. The earlier meaning comes from an old Dutch term for palming a loaded die into a game. Today we call that cheating.