I was messing about with the fanatic (in a FEA mixed team) and pushed a chaos dwarf off the pitch while he was downed. He got stuck off the pitch, and wouldn't stand up (AI controlled.) The game would save and load fine, but that player couldn't do anything. I didn't score a TD to find out if he reset correctly.
(PC) Ball and Chain can push downed players off the pitch, where they get stuck.