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.
The setting in which Harry disappears and returns also matters. If it's in the middle of Hogwarts, the school would be in chaos. Teachers would be trying to keep the students calm while secretly searching for Harry. And when he returns, the reactions of different houses - Gryffindor being relieved and proud, Slytherin perhaps being suspicious - could add more layers to the story.
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 some fanfictions, Harry's disappearance could lead to the discovery of new magical powers or places. Maybe he stumbles upon a hidden magical realm while in hiding. This new place could have its own set of rules and powers. As he tries to figure out how to get back to Hogwarts or deal with the situation that made him disappear in the first place, he has to learn about these new powers and make alliances with the beings in this new realm.
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.
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.
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.
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.
The theme of sacrifice could also be present. Maybe Harry disappeared because he sacrificed himself for a greater good. And his return could be a sort of resurrection, where he has to deal with the consequences of his sacrifice and how it has affected the wizarding world.
Well, in such a fanfiction, Harry might disappear to train in some hidden place, away from the prying eyes at Hogwarts. Maybe he goes to a secret location with a powerful wizard who teaches him advanced magic that he couldn't learn at school. This could include dark magic defenses or ancient spells.
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.