Ingragonaza,
sorry for spelling,,,
It does sound pretty severe in problems there. I am sure you admire him for wanting to play piano and sticking with it like he has. However, if he is unsanitary at the piano like that, and you are truly concerned with his well-being - only you can truly judge the situation.
I've never had a situation like that.
If I was going to continue lessons, some things that I might do is:
1. Start a new song
2. Provide him an opportunity to play in front of friends and students that would be supportive. (I know this sounds overly optimistic, and maybe it is, but sometimes people really change when a small forum opens up like that and get more into it>
3. Come up with a goal sheet (I know it sounds crazy, but maybe he has gotten into a rut, and new goals may actually stimulate him.
4. Shorten the lessons. You may not even need to tell him. I would say I'm restructuring my lessons around people's hectic schedules and length of attention spans and feel that they will get a lot more out of the focused shorter classes. Give an example of someone you know that started getting a lot more out of a shorter lesson if you can.
5. Ask him more questions. Not all musically related, some just to get him talking about his golf game, or whatever. I have noticed that this helps some people get into their music with a new energy when they share a little bit about their life.
6. If you are a praying person, I would make sure I prayed for him and myself before each time I taught him and pray for creative ideas.
It sounds to me like this is a very trying situation - I wish you luck and will pray for wisdom for you.
He is probably on heavy medication and is doing all he can do to keep going forward.
Stopping lessons would be hard on both of you, but only you can decide what is the best. I think that would be very difficult. I don't envy you. Then again, maybe I do envy you. If your students are that committed you can't tear them away from the piano - that is saying something pretty big.