One possible scenario could be that Percy has faced so many traumas and losses in his battles against the monsters and gods' schemes that he simply feels exhausted and wants an end. For example, if he loses his close friends like Annabeth in a particularly brutal way, it might push him to the edge.
Maybe Percy discovers some dark secret about his destiny or the world of the gods that makes him think death is the only way out. Like finding out that his existence is somehow causing more harm than good to the people he loves, and he decides to sacrifice himself by asking for death.
Perhaps he has lost too many people close to him. If his friends, like Annabeth or Grover, were to die in a particularly tragic way, he could be so grief - stricken that he no longer wants to live in a world without them. He might think that death is the only way to escape the pain of their loss.
One interesting scenario could be Percy facing off against a powerful demigod from another pantheon. For example, if he were to battle a Norse demigod, the different powers and fighting styles would make for an exciting story. Percy's water - based powers against the ice or thunder - related abilities of a Norse counterpart would create intense battles and strategic challenges.
One possible scenario could be that in the fanfiction, some evil organization captures Percy and tries to figure out his powers related to being a demigod. They might subject him to various tests like trying to measure the limits of his ability to control water, or how he can heal from injuries that would be fatal to normal humans. Another could be that they experiment on his connection to the Greek gods, perhaps trying to sever or manipulate it in some way.
Perhaps in a scenario where Percy is about to sacrifice himself for the greater good. Triton, seeing Percy's selfless act, is so moved that he cries. Another situation could be when Percy is being wrongly accused and is facing great danger, and Triton, who knows Percy's true nature, cries out of frustration and worry for him.
It could be a new, powerful and malevolent god. This god might be jealous of Percy's status as a hero and the favor he has from some of the Olympian gods. So, the new god devises a plan that makes Percy's life so miserable that he asks for death.
In a 'Percy Jackson Dies' fanfic, one possible scenario could be that he sacrifices himself to save his friends during an epic battle against a powerful new enemy. Maybe a horde of monsters that are immune to his usual powers overwhelm him while he's trying to buy time for his friends to escape.
Well, Percy might die in a magical accident. Maybe he's trying to harness some extremely powerful and unstable magic, and it backfires on him fatally. He could also be the victim of a curse. A powerful sorcerer or a vengeful god could place a curse on him that slowly kills him. And in some fanfictions, Percy could be killed by a group of enemies who gang up on him when he's in a weakened state, like after a previous battle or when he's separated from his friends and allies.
One possible scenario could be that Percy dies heroically in a battle against dark wizards. Maybe he sacrifices himself to save his family or a group of innocent people. Another could be that he succumbs to a mysterious and incurable magical illness that has been plaguing the wizarding world. He might have been researching a way to stop it but in the end, it gets the better of him.
One possible scenario could be Percy being betrayed by a primordial who he thought was an ally. Maybe the primordial promised him power to defeat a common enemy but then turned on him at a crucial moment, leaving Percy vulnerable and alone against a greater threat.
One possible scenario could be that Percy sacrifices himself to defeat a powerful enemy. Maybe he uses his powers to hold off a huge monster that is about to destroy Olympus and in the process, he gets fatally injured and dies. Another could be that he is betrayed by someone he trusts, which leads to his death. For example, a demigod who is jealous of Percy's popularity and powers might make a deal with the enemy and set Percy up.