Describing prison as "housing at taxpayer expense" is... one way of putting it.
I think they should be given a choice: go to jail or get a job and 2 months of state funded housing. If you go back on the streets because you didn't want to work, then police will pursue every public nuisance, public urination, shoplifting, etc. charge and send you to jail. If you're mentally ill you're forcibly committed. If you're a drug addict, you're forced to go to rehab or go to jail.
Otherwise these people will never learn to be decent members of society (you know, people that don't steal and shit on the streets - the bar is on the floor).
A lot of these people don't want to go into shelters because those shelters have no drug use/no alcohol policies. But I say the state should not be supporting their drug habits with taxpayer dollars.