We'd obviously want to model it around something like Arkansas. Remember, prison provides reasonable security, food, and clothing. Security will generally be better since regular people are not self-selected for criminality, and those savings can be moved over to improved food. Re-using the prison model for extreme low income and homelessness is not intuitive - but so be it (sometimes you have to use an anti-pattern).

Edit:

$100k/prisoner/year

That's crazy. Regular people don't live on that yearly.

How much of that is surrounding infrastructure and overhead (guards, security, etc) that don't apply? Plus that includes all meals, medical care, instruction, and other resources in many cases.

Humor aside, there are people in the US who do get arrested for misdemeanors on purpose just to spend the night in a warm jail, and those that try to get into prison to alleviate chronic homelessness