I read in a book one time that we should never forfeit a game. If you find yourself in a losing hopeless situation, you should stick it out and play to the end, for no matter how small the chance, there is always the possibility (remote as it may be) that your opponent might fall dead of a heart attack rendering you a victory by default.
Besides, we should never flick over the king to signify surrender, for a king knocked over represents death, and we should never allow a king to suffer the indignity of death. That is why we only capture the king in checkmate. In the end, he is still alive.
At the end of the game, after I've captured all my opponent's pieces, I place them in an internment camp, and from there I commit a small-scale genocide, king included. I burn or melt the pieces, depending on what they're made of, and if I can't burn or melt them, I break them.
The upside for my opponent is that they can't lose twice to me. A potential downside for my opponent would be that if they owned the chess set, they now only have half a set. But hey, they took the risk of facing me, not my fault.