Some guy on reddit has talked repeatedly about getting a tax lien home for just under $800 to end living in an RV and get back into permanent housing:
Probably the same guy: I am no longer homeless
Of course, there will be ongoing utilities, likely substantial repairs will be needed, you will have other ongoing expenses like property tax and homeowners insurance, but if you have no house payment, it gets a lot easier to cover stuff like that and you can shop sales, DIY some stuff etc. to keep it affordable AND you can have some say in exactly how it gets resolved, something you tend to not have when renting.
If you have some income, especially something portable such as retirement, disability or remote work, and some latitude as to exactly where to live, this may be a path to a stable, middle class type lifestyle on a budget.
I actually wanted to do this and didn't pull it off. While on the street, I researched it some and subscribed to https://www.bid4assets.com/
When I found the site, it was free to sign up for. A lot of tax lien sites I found were charging a fee to register and access their info.
You can surf the site for some info without signing up, or could a few years ago. I haven't looked at it recently and the site looks a lot different than what I remember.
There is this oft repeated meme online that "The US has plenty of housing! There are lots of homes sitting empty, more than how many homeless people we have!" and it is typically used as another excuse to blame homeless people as not trying hard enough.
Currently, the US does a very poor job of helping homeless people get back into housing. It takes substantial individual research to find opportunities like this and anyone good at it tends to be someone buying up properties for commercial owners renting them out at nosebleed prices.
If you really want to make a dent in homelessness AND fill existing vacant properties rather than advocate for development of more affordable housing, you could try to find ways to help homeless people get into tax lien homes.
For some people, this is potentially a more immediate solution than trying to get new apartments built of the right kind and blah blah blah. (For other people, the housing they need simply doesn't exist and we NEED to build it.)
A few provisos:
It's not for everyone, so don't act like it is. It can help SOME people but won't "solve homelessness."
I don't drive anymore. This contributed to my failure to get a tax lien home or other bargain property: A lot of bargain properties are in the sticks and there is no bus service, so won't work if you don't drive or don't own a vehicle.
Bargain properties typically require cash upfront, which is hard to come up with if you are already homeless. Poverty is expensive, so it's tough to save, and if you get benefits like food stamps, saving too much can disqualify you from receiving them and now you are back behind the 8 ball financially.
Some other potential bargain properties:
FSBO: For sale by owner. This eliminates or reduces the fee for the real estate agent and some will finance it, so you may not have to qualify for a conventional mortgage.
Homes with certain kinds of defects: When I was researching buying a cheap house to get off the street, I came across a listing for a house selling for $10,000 because it had no foundation and would not qualify for a mortgage.
Of course, it was cash upfront, in the sticks, with no bus service out there. No, none of that worked for me. But that doesn't mean it won't work for someone else.
"Luck favors the prepared." If you can research this, you may eventually fins the right opportunity for you.
And maybe someday our government will pull its head out its butt and stop making real estate a great deal for monied predators and figure out how to more reliably help put cheap properties into the hands of poor people so they can be homeowners instead of homeless.