I'd expect my opponent to resign when they have at least a -10 material disadvantage. But I don't insist on it. It is a bit silly (and possibly rude) hanging on a game when you have only your King and 1 or 2 pawns against overwhelming forces. And if they are hoping for a stalemate I am a lot more careful now.
Strategists vs Tacticians - and the expectation that opponent must resign
I like it when my opponent doesn't resign in a hopeless position/theoretically won endgame - I find switching to autopilot and converting the win quite therapeutic!

I'd expect my opponent to resign when they have at least a -10 material disadvantage.
It is a bit silly (and possibly rude) hanging on a game when you have only your King and 1 or 2 pawns against overwhelming forces.
The mate is quite simple by the way as you can see(epaulette mate). It is entirely forced and there aren't even variations to consider. Further, Karpov could have always captured the black pawn, promoted the pawn to rook/queen and delivered a rolling doublequeen mate.
And if they are hoping for a stalemate I am a lot more careful now.
When the great Karpov can blunder, why should your opponent expect that you won't?
Further, why don't you consider it a test of your end-game skills? The ability to end the game is also a very important skill. Just because an end-game is a theoretical win, that doesn't mean that it will always translate to a win. Many things can happen.
Cheers and peace :)

you paid for your own entry fee: you can do whatever legal action you want
What your opponent wants you to do should have no bearance on what you actually do (mind the legal premise)
Thus, if you want to give up, give up, if you don't want to give up, then keep fighting!

I've had opponents manage to force draws by stalemate or repetition in "lost" postiitons often enough (meaning once in a hundred games, is still often enough) that I have changed my own approach and play on much longer than I used to. It used to annoy me when people played on since it felt they were looking for a cheap swindle but now I take it more like--"if the game is a forced win, show me. If you can't, you don't deserve it anyway."

I only resign when I know I have no chance of winning, and I know my apponent is not prone to blunders. If there is any chance of a stalemate, I will hang in to the bitter end. There is a lot that can be learned in the final stages of a game, whether you are winning or loosing. I have found that a lot of players are not that great in the end game. You can not take advantage of this fact unless you play the game out. I never resign, just because my apponent thinks I should.
Before I even start, I would like to state that I am mostly referring to D, C and B class level players and not Experts, Masters etc. Having said that, here is my essay.
So, I am somewhat tired of 'strategic players' expecting that people resign because the 'position is hopeless'. This so called hopeless position could be only because - opponent has no central control, and the opponent has 2 pawns less with no compensation.
Now, regarding this expectation to resign - why do I talk about strategic players. I see that its mostly the strategic players who have this expectation that their opponents must resign in lost positions - 'grandmaster style'. They hate it and whine about it when you don't resign - after you are materially or 'strategically' down and have no compensation to show. Personally I feel that this expectation is borne from the fear that the opponent might pull of a tactical stunt that will upset their game and rob them of their 'rightfully earned win'. But people will all dispute it anyway. So let us instead discuss a game.
Here is the game.
This is a well studied game and normally people would expect black to win comfortably. But that's not the case, black has a minor advantage and the game ends in draw or win for white, if black issues a sacrificial check with his Light squared bishop, and if black captures.
However, I had the opportunity of analyzing with stockfish on my chessbase and it suggested a move that could possibly lead to a draw. Note that even in a real game, I would have definitely sacrificed bishop and issued that check - not because I am a brilliant player who can see very deep, but because I don't believe in resigning tamely before exhausting even checks (thanks to Farnsworth's Predator book).
What if black rejects the free bishop?
Still want us to resign? Instead of asking people to resign, people should improve their tactical prowress so that they can issue that checkmate!