That was absolutely free, $0?
>Like some housing that was built to be closer to "indestructible" than "nice" and was small, like 200 - 300 sq ft.
We already have those housing units. They have concrete "beds", toilet-sink combos made out of stainless steel, and a thick steel door that can't be burned by arson. Nothing flammable is allowed within them (save the non-homeless person). The technology exists, and the homeless are actually welcome there. People get mad when they are homed thus, though.
Mental illness, drug addiction and homelessness all exist in a range. There are many people who are homeless, mentally ill or addicted to drugs who still have some amount of income of one type or the other.
I would try to target rent under $1,000 per month for such housing