Actually, the person who joins the game can save, as well, but if they continue playing on their own, they would either have to re-do that progress if they joined the host's game again, or they could host the game and the former host could join their game. If both players kept playing from the previous joint play session, they would either have to pick one to go with, or revert to a previous save and both start again from their last co-op session.
