The rich will bail out state pensions when they go bankrupt, and effectively already do via implicitly backing state debts.
In the end, all social security is a wealth transfer from rich to poor. Even rich employees become much (money) poorer when they retire. That's not a criticism, just an observation.
There are some other components administered by the same agency, including TANF, SCHIP, and Medicare, so yes there is some safety net there, but relative to other western countries it's rather poor. If it weren't, we wouldn't have so many homeless people. America is NOT like western European nations.