Wrong two ways: there are criminal statutes prohibiting the possession of stolen property and the owner of the money could sue to get it back, regardless of whether the government prosecutes the bad guy.

Nope, but if you find me with some of the money, you still have to prove I was the one who robbed the bank. I'm going to claim I found it on the street.

When you find someone without documentation, how do you prove when/where/if he crossed the border without documents? What if he claims he was born to undocumented parents within the US, or that he was brought across the border when he was very young?