Breja: I remember being really pissed off when after trying for a good long while I managed to escape that ambush early on in the first Deus Ex, only to discover that it's not really an option and there's no way to continue the game without getting defeated there. I guess I can't really blame the game, it's not like it gave me a choice and then ignored it, it was my own stupid tenacity that made me decide "no, there has to be a way out". I'm still kinda proud I managed it, even if it leads to nothing.
There's a few poorly designed instances of this sort of thing:
* One boss in Dragon Warrior 7 who doesn't seem to be especially dangerous (I think having the enemy use spells like Explodet was supposed to be a clue, but this is at a point where you can survive, and could realistically have the means to recover from it), but yet that particular boss has 65535 HP or so and you are meant to lose that fight.
* Lufia: The Legend Returns has one boss fight you're meant to lose, but which isn't that difficult. Fortunately, in that game, if you manage to win one of those fights, the game lets you continue and even gives you a special reward, though the game otherwise continues the same way. (There are other instances of this, but it's clear that you're not supposed to win, like the first boss fight where the boss eventually uses an attack that is not survivable at that point in the game, and it hits both your characters.)
* Final Fantasy 3's Cloud of Darkness. In the famicom version, you can cast Shell to reduce the damage you take to 1, but you have no way of doing damage, so at this point you are stuck, particularly since you have thousands of HP at this point. There's also the early Bahamut fight, who does very little damage and takes decent damage, but who refuses to die (too many HP and fully recovers every round), so it's easy to get stuck here and not realize you're supposed to run away. Both bosses were fixed in the DS version; CoD will hit your entire party for (displayed) 9999 damage in the fight you're not supposed to win.
* Final Fantasy 4 also has one boss fight where, if you forgot to pick up a certain item in town, will just do 9999 damage with normal attacks and where a party wipe is an actual game over. Only by getting that item first can you continue past that fight, and if you didn't get it before hand, you have to go back through one of the game's most annoying dungeons.