It's harder than it looks, apparently, because millions of low earners -- i.e. almost all of them -- manage to avoid this outcome. I feel like poor people are discussed in the abstract by people who have never actually been poor. Homelessness is still not a normal outcome. Mentally and physically able people are not routinely homeless.
You can try to reason through this from first principles, I guess. That's a fun thing to do on a nerd message board. But I'm telling you that this is not what happens in actual practice.