I used to manage a property for a private developer that had built an apartment project for chronically homeless people. (By chronically, they meant for at least three years homeless.)
The identified problem was that a lot of the people in my city who have been homeless a long time have mental illness that is not debilitating enough that they need to be (or indeed can get into) a long-term facility, but is severe enough that it prevents them from having gainful employment. For many of them, there was no way to schedule follow-up medical visits or other assistance because they had no address or phone.
The theory was that if they could get people into stable, independent, community housing (as opposed to facilities where they can't come and go at will) with follow-up, they could get people into proper treatment, get them job counseling and/or training, and other assistance, and eventually move them out into their own housing.
The part that really made it work was that it was a partnership with a homeless shelter that staffed the place with social workers and mental health workers. Real professionals, those folks, well trained in medical issues that might arise, and given permission to talk to and/or call people's doctors when the need came up. A lot of the residents, in fact, I'd say solidly 40%, were Vietnam vets who were entitled to VA medical benefits, but didn't have support to claim them. Two of them, after they moved in, found out they actually had outstanding pensions from their combat service that they'd never claimed.
The results were pretty remarkable. The city homeless shelter went from having an average of 100 days a year full being over capacity and having to turn people away to ZERO. With the chronically homeless population in another program, the city was able to focus their assistance on short-term emergency services designed to keep people from becoming homeless in the first place.
When I left the job, nearly half the residents had some kind of job in the community, and on average about 20% were moving out of the development and into fully-independent housing each year. It was a really great model.
So I guess what I'm saying is that for some (SOME!) people and some (SOME!) communities, and with proper follow-up and support, a housing-first model can be a really powerful tool to help people break the cycle of homelessness.