How is it that people don't starve, especially the ones with mental health problems? Or does it happen and just is so accepted it is not worth reporting?

Because food is extremely cheap. It's not good food, but it's food. You can get 2,000 calories for under $4, it doesn't take long to panhandle for $4.

On top of those half of the food available is thrown away, so those who are very motivated go and take it.

And then there are lots of organizations that help people with food, religious organizations mainly but not exclusively.

Basically if someone really needs food and is not picky about it, it's available.

People do "starve" unless they are savvy enough.

There is often help for families but not individuals without children.

When I was homeless and living out of my car I actually had a hard time getting food stamps back then (this was a long time ago). First I had the problem I was in a southern state which are mostly Republican controlled and don't want to help people. Secondly I had an impossible time proving I didn't have income (how do you prove a negative?) Then the problem I didn't have an address. Oh there was also a problem someone had the same name as me elsewhere in the state and was already getting benefits.

I showed the case worker my car I was living out of and eventually she put in some kind of emergency request so a few days later I got something.

If it had gotten any worse I would have had to turn to a church charity for help, fortunately did not come to that. It is no accident the states set it up that way so you have to turn to religion, it is disgusting.

Largely through private charity. People with mental health problems also tend to die fairly young on the streets. I live somewhere with a friendly climate to the homeless, and the chronic homeless are mostly well under 40 or retirees who can no longer make rent.