Earlier quoted context omitted.
If someone stoles cash from you, how do you mark that cash as stolen?
FWIW banks will record serial numbers of bills that go missing after a robbery.
Are they scanning all the bills that come in? Which bills are in which teller's drawer? I doubt it.
If they received new bills in sequential order from the mint and had them stolen, I could see how they would know the numbers. But then again, what's the point? Your average business isn't going to scan numbers, so by the time the bills pop up again, you have no idea the path they took.
I've heard that serial numbers from ransom money would be recorded. That makes a bit more sense as they are one-time events and there is value in knowing if you find money it came via the ransom.