There’s a patchwork of federal, state, and local safety nets with a lot of holes to fall through. Generally speaking, you have to be just fortunate enough (esp. with regard to mental health, social support, and having a mailing address) to have the wherewithal to secure the benefits, but not so fortunate that you don’t qualify. People with everything stacked against them tend to become homeless, and there are few people going out into the field to rescue them.
So there is obviously no bottom-most robust safety net, as plainly evidenced by the homeless situation. But there are a bunch of safety nets that do sustain millions of people. Welfare, subsidized housing, social security (retirement, and disability), medicare, Medicaid, to name the big ones.
In severe cases, they fall into the unable to secure benefits / care for themselves category. In the absence of consistent policy, they're at the mercy of individual psychiatrists who have sole discretion to place them in long term care, or turn them out on the street. In America, life is like a box of chocolates.
So there is obviously no bottom-most robust safety net, as plainly evidenced by the homeless situation. But there are a bunch of safety nets that do sustain millions of people. Welfare, subsidized housing, social security (retirement, and disability), medicare, Medicaid, to name the big ones.