Unwinnable

"Ethel, I think we’re fighting a losing game!"

—Lucy, I Love Lucy

'Unwinnable' is a gameplay state in which it is completely impossible for the player to finish the game. Players who have reached this point have only two options: reload a previous save—in the fortunate situations where this is possible, or start the game anew—for the much more unfortunate situations where it is not.

Unwinnable comes in four flavors:

Unwinnable by Design, where chaotic evil programmers deliberately create traps for people to stumble into. Either type has been known to prompt a Big No from frustrated gamers, and if the instance is the result of particularly egregiously bad programming, it may result in an Internet Backlash.
Unwinnable by Insanity, where the player looks at a few perfectly harmless game elements and says "Hey, if I did this highly unlikely thing, I'd break the game! Cool!" It's more of a novelty than anything.
Unwinnable Joke Game, where the game is intentionally impossible from the beginning, generally played as a joke on the player.
Unwinnable By Mistake, where bad design oversights or bug-filled programming stop the player from progressing, prevent the player from accessing needed equipment, or otherwise make the game impossible to beat.

Examples go on the subtropes above.

Compare Luck-Based Mission and Controllable Helplessness, as well as Endless Game. See also "Wake-Up Call" Boss.