Perhaps Harry is kidnapped by a mysterious and powerful magical being. This being has the ability to make Harry disappear without a trace. His friends then embark on a dangerous quest to find him, facing many magical challenges along the way. They might have to search in hidden and dangerous parts of the wizarding world that they have never been to before.
It could be that Aang disappears because of a prophecy. He might believe that by disappearing, he can prevent a catastrophic event from happening. His friends, not knowing this, embark on a journey to find him, facing many challenges along the way. They might discover secrets about Aang's past that they never knew before, and these secrets could be the key to bringing him back.
Maybe he discovers a dark secret about his past and decides to run away to protect his friends and Hogwarts. He could have found out that Voldemort has some new evil plan related to him specifically on his 16th birthday.
In fanfiction, if Harry Potter disappears, it could lead to chaos at Hogwarts. His friends like Hermione and Ron would likely be on a desperate search for him. They might suspect the Dark forces at work again, and start investigating all the possible places where Harry could have been taken or hidden.
One possibility could be that Naruto is kidnapped by a hidden enemy right at birth. Maybe a rogue ninja group has a vendetta against the Fourth Hokage and they steal Naruto away. This would lead to a completely different story arc in the Naruto universe, with Konoha perhaps not knowing Naruto's true identity and not treating him as the Jinchuriki. It could also mean that Naruto grows up in a different environment, away from the discrimination he faced in the original story, but also without the friends and support system he eventually had in Konoha.
Voldemort could be the antagonist. Even if he was defeated in the original story, there could be a scenario where some remnant of his dark magic causes Harry and Hermione to disappear. Maybe he had a secret plan that was set to activate after his death and it involved taking them out of the picture.
It could be a new dark wizard who has been secretly plotting in the shadows. This wizard might be jealous of Harry's fame and power, and decides to make him disappear so that he can rise to power unopposed. He could have a group of followers who are experts in dark magic and are able to carry out his plan to make Harry vanish.
Well, it could be that Ash disappears on a dangerous quest. His friends in the harem are distraught. When he returns, he might have new powers. And then he has to deal with the changed dynamics in the harem, like some might be angry at him for leaving, while others are just overjoyed to have him back.
One possible plot could be that Percy is betrayed by one of his closest friends in Camp Half - Blood. Maybe Annabeth turns on him out of jealousy over his growing powers or a misunderstanding. Percy, feeling deeply hurt, decides to disappear into the mortal world. He cuts off all ties with the demigod community and tries to live a normal life, but his past keeps haunting him as monsters still sense his presence.
Well, it could be about a magical curse. Maybe an evil sorcerer casts a spell on the castle and it slowly fades away. The characters then have to go on a quest to find a way to reverse the spell and bring the castle back.
Well, he might disappear because of a powerful curse from an ancient enemy. Maybe he gets trapped in a different dimension. When he returns, he could have new powers or knowledge. For example, he might have learned some secret magic from the other dimension that helps him defeat a new threat in the Percy Jackson world.