Would it be at all possible for your son to live with you? 

I hate to be the bearer of bad news, but I can't help being realistic.  If your son is refusing medication and not improving then you can go ahead and wipe the phrase "long term" anything from your vocabulary.  I'm really sorry and I hope that I'm wrong about your situation!

Temporary solution #1:

If you are referring to a group home setting, then you can apply to those types of places.  Of course, even if he gets accepted, you cannot force him to go.  If he does go, you can't make him stay.  If he goes and gets kicked out, then he has earned a bad reputation in your area and any attempts to get him into another one will be even more difficult. 

Temporary solution #2:

If you are referring to low cost goverment housing, then yes he probably does qualify. All you have to do is apply, provide all of the appropriate documentation, and wait. This would be ideal until he gets evicted.  Then it would be extremely difficult to ever get back into government housing in the future.

Temporary solution #3:

Help him afford a cheap apartment.  Do not tell any agencies that you are helping.*  Encourage him to take his medication and make sure he gets to his appointments.  Hope for the best.  If he gets stabalized, encourage him to work for money, doing whatever he can, if at all possible.  Hope that he can lead a productive life and learn how to live with his illness responsibly.  I've heard that is possible, allthough rare.  If or when this doesn't work out, start over. 

Temporary solution #4:

Let him bounce from shelter to shelter until he realizes that he needs and wants your help.  Check in on him as often as possible and offer him help as much as you can.  Learn as much about his illness as you can so that you will be able to support him emotionally. 

This illness is very harsh and sometimes this is the best that can be done.  I am so sorry, I know this must be extremely difficult for you.