I wish they would make a RPG you could actually fail at

[The_Liquid_Laser]

I know for sure Oddworld: Abe's Odyssey (PS1) does exactly what the OP is asking for.  The story is pretty simple, but I can tell you my wife had to replay the whole game, because when she got to a certain point, she realized her decisions kept her from completing the game.

Dragon Warrior 1 (Dragon Quest) gives the player a key choice right before the final battle.  It's pretty easy to figure out what the right choice is, but if you make the wrong decision, then you can't beat the game (although you can reload).  Interestingly, Cuphead does the exact same thing right before you fight the Devil.  I didn't have the balls to make the wrong choice with Cuphead, because it took so long to get there and I didn't want to get screwed over by an autosave.  Back in the Dragon Warrior days I made the wrong choice on purpose though just to see what would happen (nothing really special other than you lose).

There are several Souls games where you can just kill whatever NPCs you want, and I know they have permanent repercussions.  I don't know if it's possible to make the game unplayable or not, because I haven't experimented enough to kill every NPC.  Also Neverwinter Nights is a game designed for player made adventures.  I'm sure there are a ton of games there where you can kill key NPCs and make the game unplayable.

In Final Fantasy Tactics if you don't have the proper abilities and party setup before going on the Wiegraf string off battles then you can get into an unbeatable situation.  There are enough battles in this string that it is pretty common that people have saved over all possible saves that would allow them to level up through grinding.

Lastly, I have to say that I still haven't beaten the genocide run of Undertale.  When you go that route certain fights become a whole lot tougher.  I still haven't beaten the final tough boss, because he's just that tough.  If I go any other route then the game is easy enough to beat, but the genocide run is hard enough that it's really, really tough to finish the game and therefore get any ending.