@TBest, what chess site do you play on? I play on gameknot.c o m and below are quotes of their general help
Q25: My opponents is refusing to resign a lost game, what can be done about it?
A: Unless any of the chess rules or any of the GameKnot rules have been violated, unfortunately there is nothing that can be done about the game. If you find someone's behavior annoying, please simply add that person to your ignore list. You'll still have to finish the game though, so the best solution is to remain calm, always make your best moves and crush your opponent on the board.
Q26: My opponent is delaying a lost game, what can be done about it?
A: Every player is entitled to make their moves at any time as long as it is within the time control set for the game. Unless any of the chess rules or any of the GameKnot rules have been violated, unfortunately there is nothing that can be done about the game. Using all the time allotted to the player is not against the rules, nor is it unethical in any way. While it might certainly be annoying, however in most cases your opponent is not actively trying to annoy you personally.
Players may take longer to try and find a way out of a tricky situation, looking very carefully to find a saving move or exchange, which takes time. Once in a while you may come across players who, in your opinion, are dragging out a "lost" game. However, they might not realize that the game is lost for them, or they might have something planned that will change things around very soon, or they might simply be trying their best to come up with a solution, which might or might not exist. Surely you will also appreciate being able to use all the time allotted to you to make your next move, when you find yourself in a difficult situation on the chessboard at some point in the future.
There are also players who generally are not in any rush to make their moves, who prefer to take their time when playing. You can always check the player's stats page, by clicking on their username, to find their "average time to move" stat, so that you can avoid slow players. If you still find someone's behavior annoying, please simply add that person to your ignore list, so that you don't have to play them again in the future. You'll still have to finish the current game though, so the best solution is to remain calm, always make your best moves and crush your opponent on the chessboard.
There is no indication about any kind of punishment for stalling. There is even explicit statement
Using all the time allotted to the player is not against the rules, nor is it unethical in any way.
Furthermore below is quote from their official tournament rule.
Purposefully losing or tying tournament games, before the logical conclusion of the game, will result in disqualification of all players involved from the tournament.
Actually, in some circumstances, we could be in danger if surrender too soon.
So, either we play on different sites with completely different rule of we have completely different interpretation of same/similar rule.