I think a great way for players who abandon an adventure early (Choosing not to explore and waiting for the blessings deck to empty) when low on health points (to hopefully avoid dying) should have a penalty applied to them. Basically risk/reward to keep it interesting... you wouldn't want it to be automatic.
How about a wandering Monsters roll?
Any player who chooses not to explore on his turn (Outside of using powers like Kyra's healing etc) rolls a D6. On a 1 or a 2 he has to draw a random monster from the box and encounter it.