There are exceptions (see other comments), but between good players they almost never allow the other player to get a better position after giving up the piece. That is they see the attempted sacrifice and how much worse (better for the other player) the board is afterwards and don't take it. Thus most piece losses are a blunder, and they know that the opponent knows how to win (unless they make a return blunder, which is unlikely).
That is at the high levels. I play my down positions, because I'm not playing anyone that good. I learn a lot and my opponents often enough will make return blunders I can take advantage of. (I typically lose anyway, but it works out often enough to be worth trying)
One other consideration: in a tournament situation it might be better to resign and take a nap. You can then come into your next game well rested while your next opponent might be worn out from his last game. A loss and a win is better than a low odds chance at a draw but probably a loss and a game that you play tired and so have decreased odds of a win and might lose as well. Psychology like this can be important.
That is at the high levels. I play my down positions, because I'm not playing anyone that good. I learn a lot and my opponents often enough will make return blunders I can take advantage of. (I typically lose anyway, but it works out often enough to be worth trying)
One other consideration: in a tournament situation it might be better to resign and take a nap. You can then come into your next game well rested while your next opponent might be worn out from his last game. A loss and a win is better than a low odds chance at a draw but probably a loss and a game that you play tired and so have decreased odds of a win and might lose as well. Psychology like this can be important.