If you're saying that "homeless" means something other than not having a home, that seems unnecessarily confusing. Re strings - I believe there has been some success in providing no-strings housing and then working on the other problems.
It's a broad term, just like "Sick" can mean anything from having a seasonal cold, to terminal cancer. The causes vary, the prognoses vary, the treatments vary. Talking about "Sickness" without specifics is profoundly unhelpful.