There are those few adventure cards that have you draw from the Dungeon deck instead of the normal deck. When you draw a card that you are supposed to ditch when you leave the dungeon, does it stay with you until you enter and then leave the dungeon, or do you immediately discard it after encountering it?

Bring that hunchback home, yo. He got lost in the woods and will stay with you until you guide him to the dungeon.