This concept probably already exists, but under a different, better name. It is what I think role-playing games are often intended to be, but tend not to be designed to be.

The idea is that instead of players being primarily focused on playing their characters, and keeping their characters alive and successful, and in solving problems in the best, most resourceful way, the players are focused on bringing about situations in the game that are thematic or that emulate features of the genre in which the game is set.

The basic example would be an adventure game in which players battle monsters. The goal of the players in a monster battle scene would be to bring about a scene in which the monster got to be terrifying and hard to beat and that the characters could only hope to drive it off. This might mean that some of the characters are killed or seriously hurt, or that the characters wind up in a much worse situation, or even that one character has to do something stupid or even antagonistic. But in this kind of game those things would happen and the players would be happy, because the scene was thematic, rather than sad or angry because their characters were sad or angry.

I'm sure people have had this kind of situation arise in a typical roleplaying game, but in my experience, the players work very hard to prevent the monster from getting the upper hand, with the result that the monster generally looks pathetic and sad as the characters beat it up and prevent it from getting away. Any player whose character does something stupid or counterproductive is, in my experience, berated, even if such an act is exactly the kind of thing one might see in a movie or read in a story.

So, do such games exist? Or is it purely reliant on the players, regardless of the rules being used?

Honestly, what you're describing sounds more like a novel, or a movie, rather than a game.
In novels and movies, the plot tends to get to a climactic confrontation, where good and evil are evenly matched and the battle is hard fought and on the edge, often at the expense of the protagonists.

I agree with Nuric. The very essence of an RPG is to take the roles of other personas. Your idea flies in the face of that basic tenant. I have been playing RPGs for twenty-eight years with many different groups. I've never ran across anyone who didn't want their characters to succeed and overcome the obstacles placed before them. While RPGs do have themes, I've never played in or heard of anyone playing in a game where the theme trumped the characters. Sorry, the concept is just completely alien to me in the context of a role-playing game.

Games like that are very difficult to create, because they almost never revolve around an equal group of adventurers.  Through either varied skill or experience through the story, they will all diverge.  Very, very few players are wiling to play in a game like that.  And on rpol at least, there aren't many groups of players and GMs that know each other well enough to trust each other to create a game like that, that is still enjoyable for everyone.

More modern, more narrative games tend to do this pretty well.  FATE based games, for instance, rely on an ebb and flow of putting your character at disadvantages to gain later advantages.  The same for PbtA games where most successes come with a cost.

Those are a little more mild than your example, though.  Games that actually seek to go that badly tend to be collaborative fiction more than games.

You're right, but that's sort of the point. D&D, for example, is set in a quasi-Tolkien world. There's even a game actually set in Middle Earth. There are Star Wars roleplaying games. The clear implication is that the game will emulate those stories. They tend not to, in my experience.

That's why I tried to use a new term.

When I play a roleplaying game, though, I want my characters to succeed and overcome obstacles, but not at the expense of the theme. There might be a better way to succeed than going up against the evil wizard, but going up against the evil wizard (and for the evil wizard to get in some good hits) is the point. So, you've now met someone who would be willing to trump his own character.

I get what you're saying, but I think that much of that comes from the fact that the focus is on the individual character. If the goal was interesting situations, then how good or bad a given character was wouldn't matter.

I'd be fine with that, or even with a hybrid version of it. Do people play that way? Do people apply some rules to it?

Thanks for the responses.

Fate games are intended to allow this (it's the basis of the Fate Point economy), with things going poorly at first so they can go better later on.

What you seem to be looking for is Fiasco. It's designed to run Reservoir Dogs and the Big Lebowski type things, where stuff just doesn't goo well for anyone and seeing the chaos play out is the fun of the game.