No, you can't fully tie an address to an individual. Especially if the money is spent into the economy beyond.
You could invalidate addresses containing the fradulent funds, and generate Bitcoins from nothing into a new address, so for example block 5000_from_now puts 20k BTC into a particular address, and the private key for this address (the wallet) is given to allinvain. Mining creates BTC from nothing so you could use a similar mechanism.