We have social housing. In places like New York City, public assistance developments have historically tended to be big tower blocks of housing that seem to become run-down and unpleasant and sometimes pretty dangerous fairly quickly. (These are what people mean when they say "the projects." Many if not most are still in operation I think.) These days there's more going on in the way of rent vouchers on "normal" apartments; some cities have regulations now where if you build an apartment building, x% of the apartments have to qualify for public assistance rent, meaning the rent can't exceed x and you have to take tenants who are on assistance. I don't know all that much about this though, sorry.
In general I am sorry to say (and my experience with this is limited, so I really may be off here) that I think people here are often ashamed to be on welfare. This is b/c we have a history of people on welfare being stereotyped as lazy. I think this perception mostly comes from some nasty political positioning, e.g., en.wikipedia.org/wiki/Welfare_queen.
Some people certainly game the system but I think that's more b/c it's incredibly hard to get off welfare: if you earn above $x, you don't qualify for welfare anymore, but $x is really, really low, so you will not actually have enough money to live if you get a job. Oversimplification, but a real problem.