I agree you need the stick. In this case if people are refusing housing due to drug addiction or another mental malady then they need to be institutionalized. I think the choice you give them is easy, they can go to housing, they can go to hospital, or they can go to jail. Which do you want?

And obviously you take their drugs away from them. I'm somewhat keen on the idea of not tossing drug users into prison en masse as I don't think it helps much but that only works if you actually have cops arresting and confiscating drugs from everyone who even tries to use them in public.