I saw somebody report a champion getting cracked skull and dying, not sure if the two were related. They didn't get knocked out or escape, they just died and stayed dead. It sounds like a bug, but maybe if they hit -1 exp they disappear.
The realm of negative experience must be a scary place indeed. It's basically saying: "Wow, you're not even good enough to be level 1. LEVEL ONE. You don't even deserve to live, get out of here!
Or else maybe they could just get downgraded to level zero, and then when leveling up again they can choose to specialize as a hero or a caravan.