I take from your post that your cousin is moving out with a love interest? There's not much that can be done about that that you probably haven't already tried to do.
If it were me, I would look at it as a "clean slate" and move out too. If I were single, I'd look to rent a room or take on a caregiver position that offered free room and board for "overnights", meaning that I would have the days and weekends to myself, but would be available to help if the person needed it overnight.
I would ask any friends who might be interested if they would like to move in or put an ad out now for a roommate and begin screening.