What if ....
Someone was a bit nonchalant and did not back up his/her coins, but ... But he/she remembers his/her private key. Is there a way to 'restore' these 'lost' coins? IOW, is there a way to match private key and a specific address in the block-chain?
If you know the private key, then you can access the coins:
https://en.bitcoin.it/wiki/Private_keyJust as if you wrote the key down or printed it.