I know there is a couple of instances that’ll make me not want to complete a game (win or lose).
1) Exploration: If there is a lot of things in the game that I need to collect, or if there is a different play through of the game that I can explore (without having to restart). These things really keep me from finishing a game and instead put me in the mode to collect as much as I can.
2) Frustration: If a game is way too “punishing”. I don’t want to take the time to complete it. A game that doesn’t make me feel like I’m getting anything out of the experience is one I don’t want to waste my time on.
3) Boredom: If a game can’t hold my interest. I usually will not try to win it at all.
If there is any way to create a game that will try to prevent you from winning, it would probably be akin to the first option. Games usually have “multiple” endings, and each of those endings can be associated to actually “winning” the game. Of course, I am associating “winning” to actually mean “completing” the game. A game that awards you for losing would be a good example of this.
To be honest, getting a person to morally not want to complete a task can be as easy as making that choice very unappealing. You can be direct by just preventing them from entering a room via an invisible wall. You can be indirect by making the boss of that room impossible to defeat. Getting someone not to complete your game really takes a lot of work, turning it into an endless grind. An MMORPG as it were; Something where you can spend hours of time and never essentially win.
However, in terms of emotion, you would need to give the antagonist as much impact as the protagonist. You would have to get the player to feel emotionally invested in both characters of the story. Both of those characters would have to be correct, and the choice would have to be very debatable between both parties. A game like that would really need to be stellar in order to pull that amount of depth out of two characters, though it could be possible with a group (like Mass Effect managed to do with its choices).
Thinking about it, making a game that is very easy to win might be engaging if you can see how long you can last without winning. However, then you’d just be using a cheap sense of reverse psychology. 