I think I've seen the study you're referencing, or at least a similar one that looked at California.
The one I remember found that as cities focused on a "housing first" model to combat homelessness, they wound up spending more money over time because the programs aren't effective in the long term. Again, Latte liberalism says "if they have a place to live, they aren't homeless! Job done!".
A large portion of the homeless problem is tied to mental health/addiction issues, or education/housing markets being dogshit.
The stat is a year or so old, but I do remember that roughly 20%-25% of the people living in the homeless shelters here actually had full time jobs, but they can't afford a place to live because of the market. Every attempt to build more multi unit housing that's affordable gets shot down, but it'd be super helpful to balance the market out. Our cost of living is starting to surpass Denver.