He could feel a sense of guilt. Sasuke might think that his actions or their relationship issues pushed Naruto to leave. He may then set out to find Naruto, not only to bring him back but also to resolve their long - standing issues. For example, if there were unspoken words or unresolved fights between them, Sasuke would see this as an opportunity to set things right.
They could face challenges from the ninja world's authorities who might see them as deserters. Other villages might try to capture them to gain an advantage over Konoha.
They might stumble upon a hidden village with a unique culture and way of life. This could lead to them learning new values and bringing those ideas back to their own village in the future. They could also meet new characters who become their allies or mentors along the way.
In many such fanfics, Naruto's character often becomes more vulnerable yet also stronger in a different sense. His pregnancy makes him rely on Sasuke more, but at the same time, he is determined to still be a great ninja. Sasuke, on the other hand, becomes more nurturing. He steps up to protect Naruto and the unborn child, showing a side of him that was not as evident before.
In the sasunaru context, perhaps a rift between Sasuke and Naruto makes Naruto feel like he needs to leave to sort out his feelings. He might think that staying in the village constantly reminded of Sasuke and their complicated relationship is too much to bear, so he leaves to find his own path and hopefully reconcile with Sasuke on his own terms.
Perhaps Naruto in the Anbu has a personal mission that goes against the village's orders. For example, he might befriend someone from an enemy village who is actually innocent but is being targeted by Konoha. When the village refuses to listen to his pleas, he decides to leave. He'll use his Anbu abilities to protect his new friend and find a new place where they can both be safe, away from the political drama of the ninja villages.
There's 'A New Beginning' which is another interesting one. In this fanfic, Sasuke is very protective of Naruto during his pregnancy. It shows how their world changes and how they adapt to the new roles. The story also has some exciting plot twists related to the shinobi world and how they balance their personal and ninja duties.
One possible reason could be a difference in their goals. Sasuke has always been on a journey of revenge and self - discovery. If in the fanfic, Naruto's path starts to conflict with Sasuke's in a way that Sasuke can't tolerate, he might leave. For example, if Naruto decides to fully side with the village elders whom Sasuke distrusts, Sasuke could see this as a betrayal of their friendship and leave. Another reason could be an external threat that forces Sasuke to leave to protect Naruto. Maybe there's a powerful enemy that specifically targets Sasuke and he doesn't want Naruto to get caught in the crossfire, so he leaves without explanation to keep Naruto safe.
Perhaps they leave because they discover a new threat that the ninja villages are not taking seriously. Naruto and Sasuke decide to take matters into their own hands. They travel to different places, gathering information and allies. Their relationship also evolves during this time, from just comrades to true brothers who understand each other completely.
One possible interesting plot could be Naruto's internal struggle as he leaves the village. He might be torn between his loyalty to his friends and his need for self - discovery. Another could be how Sasuke reacts to Naruto's departure and whether he tries to stop him or goes with him.