[How nice that this is getting downvoted. It's a legit question. I have family members who are social workers and know these services exist, and it seems like it's most cities, but don't know for sure, hence the question mark.]
There's a toxic culture in the USA that looks down upon welfare. For those people, welfare doesn't exist, even if they find themselves in that environment. And since they've convinced themselves that they'll never take welfare, they expect others to follow by their own rules.
This culture leads to a particular anti-welfare voting pattern.
This is coming from someone who has never lived in a shelter, so I may be wrong, but it's definitely my fear and a source of motivation when working not-great jobs.
What does happen is that charity groups like catholic churches or st vincent de paul will buy homeless and runaways one-way tickets, but only if they have a verifiable destination.
has examples of several cities that do this, not just charity groups