Shooting at another enemy, then possessing that enemy until death isn't a failure state, but self shooting is. This logical gap has me annoyed. If you are wanting to avoid suicide topics, the in game lore could be "You fail if the body you are in dies." and change it such that receiving a bullet from a different enemy still results in a loss.

When you fail, I think there should be a message along with the retry menu that states why you lost. "Hostage died." "Possessed body died." "You got shot." "Clipped by airplane wing." Most of the time it was obvious to me, but if the player isn't looking in the "right" direction, they might not know why. In the sign falling down level, I saved the two hostages, setup a kill, and then saw a "third" hostage get crushed by the sign. Not sure how one of them glitched back to starting area, but if I hadn't noticed him under the sign, I'd been confused as to why I lost.