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.
One possible plot could be that they disappear to a parallel magical dimension. In this dimension, they have to learn new forms of magic to survive and find their way back home. Maybe they encounter strange magical creatures that are unknown in their own world.
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.
Perhaps a powerful magical being from a different realm is the antagonist. This being might mistake Hermione for someone else or see her as a key to something in the wizarding world. So, it uses its magic to make her disappear. This being would be very difficult to defeat or negotiate with, making it a huge challenge for those trying to find Hermione.
Well, in some 'Hermione Disappears' fanfiction, it might be that she is targeted by a group of anti - Muggleborn wizards. They manage to make her vanish using some dark magic. Her friends, Harry and Ron, then start a frantic search. They might follow a series of mysterious clues she left behind before disappearing. It could also be that a time - traveling mishap causes her to disappear from the current timeline and she is stuck in another era.
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 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.
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.
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.