There is no way to steal people's BTC, you can only prove ownership of BTC if you have the private keys; if there was a way the network allowed people steal BTC's that don't belong to them, then BTC would have been dead by now.

There is no way to know that BTC in an address is lost, even if the funds have not moved for a very long time, it could be that the owner of the funds is a long term holder. There have been too many posts of late about lost BTC and how to recover or collect them like this op said, lost BTC are lost and they reduce the circulating supply and make your coins and mine worth a little more.