My personal opinion is that governments should provide a backstop guarantee for tenants, to bear the risk instead of forcing landlords into making cruel choices.

I think it'd make sense. It's beneficial to govt. to keep people productive and ultimately off the street. Hence (in a capitalist system) they want to encourage the market to provide housing to people who would otherwise not get it. If the government came involved into transactions as a guarantor for people in need, and provided incentives and reassurances to landlords that they would not be disadvantaged if they provide housing to those in needs, I believe there would be less homeless people in the street, and more generosity from landlords.

E.g.:

(1) if I have no upside and a high risk exposure in providing housing to a recovering addict, will I do it if I'm then unable to evict that person when they fall back down into addiction? No, I wouldn't, even if in my heart of heart I wish I could help them.

(2) if on another hand, the government came and said "we'll guarantee this market rate, and will facilitate eviction proceedings and pay for repairs if things don't work out", would I be willing to risk it and rent to that person? Probably yes, there would be enough structural support to encourage me to do some goodwill help.

The problem is that the stick presented in (1) is what's going on right now, and there's no carrot (2). It's basically the policy makers telling landlords: all you, don't you dare taking in tenants who are a higher risk! Because if you do, we'll be watching!

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In coordination with this, I think a smart policy would be to combine this idea with something else: instead of trying to build affordable housing projects, try to spread these initiatives around. Avoid the creation of ghettos. If a govt. agency was to support someone's tenancy, the agency should try to spread these people uniformly around town, mixing them with all strata of society, instead of putting all these people in the same geographical area. This would encourage reintegration in a constructive environment. People living in their walled gardens would be annoyed, but ultimately, the people in need of help would be allowed a chance to heal in a safer environment.