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.
Another option is that a new character introduced in the crossover could be the main character. For instance, in a Naruto - Fullmetal Alchemist crossover, an alchemist from the FMA world could stumble upon Naruto's sealed state and make it their mission to free him, while also getting involved in the politics and power struggles of the Naruto world.
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.
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.
One possible reason could be a misjudgment by the Hokage. Maybe they believe Naruto's power is too dangerous and uncontrollable at a certain point, so they decide to seal him away to protect the village. For example, if Naruto's Nine - Tails' power starts to go berserk and they see no other way to stop it without harming him too much.
In such a fanfiction, the Fairy Tail guild might be thrown into chaos. They could initially be confused about this strange event from another world. Some members might see Naruto's sealing as a threat to their world's balance, while others might be more curious and try to find a way to break the seal.
Maybe the village has changed a great deal while Naruto was sealed. When he finally breaks free, he has to face a whole new set of challenges and enemies that have emerged in his absence. There could be new political situations in the Hidden Leaf Village as well.
In a fanfiction where Naruto sealed away One Piece, it might have a huge impact on the characters. Luffy, for example, would be devastated as his life's goal is to find One Piece. He might even try to find Naruto to convince him to reverse it. The other Straw Hats would also be affected, their dreams of seeing the end of the Grand Line and the secrets One Piece holds vanishing. And the entire pirate community would be shaken to its core, as One Piece is like the ultimate symbol of their freedom and adventure.
It could be Orochimaru. He might have learned about the Avatar's unique power and wants to use it for his own dark experiments. So he tries to break Naruto's seal to get to the Avatar. He would be a great villain as he's always after powerful things and doesn't care about the consequences.
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.