He might be transported to a different dimension where there are no other demigods. Here, Percy is the lone warrior against the strange and dangerous creatures of that dimension. He has to figure out how to survive and also find a way back home. This would test his adaptability and his ability to think on his feet.
Well, he could end up in a situation where all his friends are incapacitated. For example, they are put under a powerful spell. Percy then has to be the lone warrior to fight against a group of evil demigods who are trying to take over Camp Half - Blood. He'd have to use his water - related powers in new and creative ways.
Well, it could be about Percy going on a solo quest to find a powerful and lost artifact. Maybe he has to face some new and dangerous monsters all by himself, like a horde of fire - breathing dragons that guard the artifact in a hidden lair.
One idea could be that Percy, as the lone warrior, has to face a new threat alone. Maybe a powerful and ancient monster that has been awakened and no one else believes in its existence at first. He has to rely on his own skills and the limited resources he has.
Perhaps an ancient and malevolent sorcerer who has been awakened from a long slumber. The sorcerer wants to use Percy's powers for his own dark purposes. He sets traps and sends magical creatures to stop Percy as he tries to figure out what the sorcerer is up to and how to defeat him. The sorcerer would be a very tricky antagonist as he can use all kinds of magic that Percy has never faced before.
In the 'Percy Jackson Disappears' fanfiction, perhaps Percy could be kidnapped by an unknown enemy. Maybe it's a new villain who has a vendetta against the demigods. This would lead to his friends, like Annabeth, going on a desperate search for him, facing many dangerous challenges along the way.
In fanfiction, Percy could be in the hospital because he was captured by an enemy and tortured. Now he's there being healed by the camp's healers or some advanced demigod medical technology. Another possibility is that he's having some sort of identity crisis related to his demigod status and it's causing him physical and mental stress, so he's in the hospital for both medical and psychological help.
Well, in this fanfiction, Percy's immortality could lead to some really interesting character development. He may start to feel lonely as he realizes that he will outlive all of his friends. This could cause him to be more withdrawn at first. But then, as he interacts with the students at Westover Hall, he might find new meaning in his immortality. He could start to see it as a way to protect others not just for a short time, but for as long as he exists. He could also form deep and lasting friendships with those who accept him for who he is, regardless of his immortality.
In the fanfiction, Percy might face new challenges related to his demigod status. Maybe he has to deal with the aftermath of the war, like rebuilding Camp Half - Blood or helping new demigods adjust.
The Titans could still be a threat. Even though they were mostly defeated, there could be some remnants or new Titans emerging. For example, a Titan who was in hiding and now sees Percy as a threat to his plans of taking over again.
He might go on a solo adventure to discover more about his powers. He could encounter new mythical creatures that he hadn't seen around the camp. Maybe he'll meet some other demigods who are on the run or have their own secret quests.
Well, in this fanfiction, Percy controlling the Styx could lead to some really interesting plot developments. Since the Styx has such a significant role in Greek mythology, it could attract all kinds of mythical creatures and gods. Percy could find himself in the middle of a power struggle as different factions either try to use him or stop him. He might also use the Styx to travel to different realms or access hidden knowledge. And perhaps he would have to face the consequences of messing with such a powerful and sacred entity, like facing the wrath of Hades or other underworld deities.