In practice, the law is not trying to 'get' people who innocently receive stolen money or goods. In the example you gave, it would be up to prosecutorial discretion what to do; trying to claw back one salary's worth of already-spent money is probably not worthwhile.
But if someone shows up and tries to deposit a couple grand worth of marked bills, they can expect to be taken into a police station for questioning, and should fully cooperate: this makes it unlikely that the penalty will extend further than confiscation of the stolen cash.
The important thing to realize is: if any of this goes to trial, the prosecution only needs to prove that the money is stolen. It doesn't need to prove the receiver knew it was stolen; that's not what the crime is here, that knowledge makes it a worse crime, accessory to robbery.