Well, in such a fanfiction, it might lead to a darker timeline for Konoha. Since Naruto was a source of hope later on, his absence could mean the Akatsuki has an easier time achieving their goals. They could target the village more aggressively, and the other ninja villages might also take advantage of Konoha's potential weakness.
One possibility is that the story could focus on how the village copes without Naruto. Maybe there would be a different kind of unrest or a search for a new way to deal with the Nine - Tails' power. Without Naruto, characters like Iruka might have a different role, perhaps becoming more involved in trying to find a solution to the power void.
Well, perhaps in this fanfiction, the Avatar enters the Naruto universe and causes some sort of imbalance. Naruto, seeing the chaos it might bring, decides to seal away the Avatar. As time passes, Naruto starts to learn more about the Avatar's world and realizes that there are good things about the Avatar too. So he begins a journey to find a way to unseal the Avatar without causing more harm, all while facing enemies who want to use the situation for their own gain.
There's also the possibility that it was an accident. Some kind of jutsu gone wrong during the sealing process. The person performing the sealing might have been inexperienced or there could have been some unforeseen interference that led to Naruto being sealed away instead of the Nine - Tails being properly sealed within him.
One possible reason could be that his godlike powers were seen as a threat. The village elders or some powerful forces might have feared that Naruto, with his immense strength, could lose control and cause destruction. So, they decided to seal him away to protect the village and the world at large.
Well, in this fanfiction, it could be that Naruto is locked away by a powerful enemy of the village who wants to use him as a weapon later. Maybe Orochimaru gets his hands on Naruto as a baby and locks him in one of his secret labs. There, Naruto endures all kinds of experiments and hardships. But through his natural tenacity, he starts to develop unique abilities that are a combination of his jinchuriki powers and Orochimaru's experiments. Eventually, he escapes and has to decide whether to use his new powers for good or for revenge against the village that failed to protect him.
The story could also focus on the efforts to unseal Naruto. His friends and the characters from the crossover world could embark on a dangerous journey to find the key or the magic to break the seal. In a Naruto - Harry Potter crossover, Hermione might use her vast knowledge of magic to research a way to free Naruto from the seal.
Perhaps Percy discovers a secret that is so dangerous that the powers - that - be decide to seal him away to keep it safe. It could involve a prophecy that he might fulfill in a way that would change the world in a way they don't want. So, they use some ancient magic or a powerful artifact to seal him. For example, if there's a prophecy about Percy uniting two warring factions in a way that would upset the current balance of power, those in power might try to stop it by sealing him away.
In a fanfiction where Naruto is sealed away, there could be a focus on the emotional turmoil of his friends and family. Hinata, for example, might be extremely distraught and use her Byakugan in new ways to try and find Naruto. Sasuke could also return to the Leaf Village out of loyalty to Naruto and join the efforts to unseal him. The story could also explore how the younger generation of ninjas, inspired by Naruto's legacy, strive to become stronger to free him.
Maybe Naruto is sealed by a powerful and ancient evil force. During the 1000 years, the world he once knew could change completely. His friends and the Hidden Leaf Village might have long been forgotten or turned into legends. When he is finally unsealed, he has to adapt to this new world and face new threats that emerged during his long absence.
One possible plot development could be that the village is thrown into chaos without Naruto. His friends might initially feel lost but then come together to find a way to bring him back. For example, Sasuke could put aside his differences and join forces with the others, realizing Naruto's importance to the village and to him personally.
One idea could be the exploration of how Naruto's sealing affects the crossovers. For example, if it's a crossover with the Bleach universe, the seal might disrupt the spiritual balance there. Another could be Naruto being sealed in a different dimension where the crossover characters reside, and he has to find a way to break the seal while interacting with these new characters.