What happens when a Reward that is a character card loses its hitpoints?
From looking I see a thread on board game geek the card goes to the hero's trash when destroyed.

https://videogamegeek.com/thread/2074878/incapacitation-and-rewards


  2) The Reward card is killed. It is sent to that hero's trash. When that hero is incapacitated, does the trashed Reward card go under the hero's character card as well? It SEEMS that way, since no exception is made for trashed rewards in the Incapacitation rules section


The response to this in the thread is that it is correct