In Betrayal at House On the Hill, we had a player who died while having custody of the Madman. The Madman omen card states that it can't be "dropped, traded, or stolen", which are actions you can do with items. Companions, however, are not regarded as items, and players have "custody" of them. Usually, when a player dies, items in their possession get dropped in that room.
So what happens when a dead player loses custody of the Madman/Girl/Dog through death? Do they stay in the room, waiting for another player to gain custody, do they go back into the omen deck, or are they removed from the game entirely?