No, he doesn't in the official series. Fanfictions about his torture exist because fans like to experiment with different plotlines. They might want to see how Percy would react under extreme stress and pain. It gives a chance to show his inner strength or to create a different kind of character development that might not be possible in the main story. It's a way for fans to put their own spin on the character and the world.
He might use his powers in creative ways to lessen the impact of the torture. For instance, if the torture involves some form of mental attack, he could try to use his connection to water to calm his mind. Also, his demigod abilities, like his superhuman strength and agility, could help him physically resist some of the more brutal forms of torture to a certain extent. And he may also draw strength from the memories of his past victories and the people he has saved.
One common theme is the shattering of trust. When Percy is betrayed, it shows how fragile relationships can be in the Percy Jackson world. The torture aspect often explores his limits, both physical and mental. For example, in many fanfictions, Percy has to find his inner strength to survive.
People write 'Percy Jackson tortured fanfiction' to explore darker themes. They want to see how the characters would react under extreme pressure. Percy is a strong character in the original series, and by torturing him in fanfiction, writers can show his limits and how he might overcome or succumb to different forms of torture.
There might be some out there in the vast world of fanfiction. However, it's not a very common or mainstream plot. Fanfiction can cover all sorts of wild and crazy ideas, but this one is rather dark and not in line with the typical heroic natures of both Percy and the Avengers. So it could be quite hard to find, but with enough searching in the more niche or experimental corners of fanfiction websites, one might come across it.
There are several reasons. Firstly, it gives an opportunity to explore the darker side of the 'Percy Jackson' universe. The original series is mainly about adventure and heroism, but fanfictions about torture can show the harsher realities that could potentially exist in that world. Secondly, it's a way to develop Percy's character further. Through torture, his beliefs, values, and relationships can be put to the test. For example, would he still trust his friends if he was tortured by someone they introduced him to? Thirdly, some fans might just enjoy writing and reading about extreme situations as it adds an element of shock and unpredictability to the story.
In fanfiction, this would be a very dark and unlikely scenario. The Avengers are generally heroes and Percy Jackson is also a heroic figure. But if it were to happen, it might be due to some sort of misunderstanding. Maybe the Avengers mistake Percy for a threat. However, this goes against their moral code, so it would likely cause a lot of internal conflict within the Avengers group as they realized their mistake.
One popular 'Percy Jackson tortured fanfiction' might be those that explore Percy's internal struggles during his quests. For example, some fanfictions focus on his emotional torture when he has to make difficult choices between his friends' safety and the greater good. Another could be when he's tortured by the guilt of not being able to save everyone. There are also fanfictions where he endures physical torture in the hands of the villains like Kronos' minions, which makes for a very intense read.
One interesting Percy Jackson betrayed and tortured fanfiction is 'The Fall of a Hero'. In it, Percy is betrayed by someone he thought was a friend from Camp Half - Blood. The author does a great job of showing Percy's pain and confusion during the torture scenes. It really makes you feel for the character.
A plotline could be Percy having to face his own fears and insecurities while being tortured. Maybe he starts to doubt his abilities and heroism. But as the story progresses, he overcomes these doubts through his willpower. Also, the fanfic could explore how the torture affects his relationship with the gods. He might feel betrayed by them for allowing him to end up in Tartarus and this could lead to a change in his loyalty or attitude towards them.
In some fanfictions, Percy's torture in Tartarus could be part of a grander scheme. For example, an enemy on the surface world has made a deal with the forces of Tartarus to weaken Percy. As he endures the torture, he gradually uncovers the conspiracy and tries to find a way to not only escape but also stop those who sent him there. His friends, unaware of his situation at first, start to suspect something is wrong and embark on a quest to find out what happened to him and rescue him.