If you have a permanent disability, there’s definitely government programs to support you indefinitely- I have several relatives on those programs (one for muscular dystrophy, one for autism) and they haven’t worked for a long time.

There’s more challenges around the short term disabilities, but pretty much every US state has a low-income / zero-income healthcare program that helps cover those individuals.

And as for overall homeless numbers, the US is pretty much middle of the pack per-capita with a lot of European countries: https://en.wikipedia.org/wiki/List_of_countries_by_homeless_...