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.
One possibility is that Naruto is on a quest for self - discovery. Leaving the village to find the Sage gives him a chance to be away from the familiar and face new challenges alone. He might encounter different types of enemies and allies during this journey. This could also be a way for him to prove himself not just to the village but also to himself. He wants to show that he can grow and become stronger without always relying on the village's resources.
Naruto might initially be in denial. He's so used to having Sakura around and believing that they have a future together. So when she leaves for Sasuke, he might think it's just a temporary thing or that she's been influenced by something or someone. But as time passes and he realizes it's real, he would be deeply hurt. He might also start to question his own self - worth, thinking that he wasn't good enough for Sakura. And he might even try to win her back at first, but then slowly come to accept the situation and focus on his other responsibilities like being a ninja and protecting the village.
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.
One possible reason could be Sasuke's pursuit of power. In many fanfictions, his thirst for greater strength might lead him to leave Sakura behind as he embarks on a solo journey to train in more dangerous and secluded places. He may feel that his goals are too dangerous for her to be involved with.
This type of fanfiction concept is really out of the ordinary. Naruto's character is built on his values of friendship, loyalty, and his dream of becoming Hokage. Killing Sasuke would mean betraying all of that. However, in a fanfiction, the author might be exploring the 'what - if' scenario. For example, what if Sasuke's actions against Konoha were so heinous that Naruto felt he had no choice? But still, it's a far - fetched and very different view from the original Naruto we know.
There are quite a few fanfics out there. One I remember has Sakura's growth as a ninja intertwined with her feelings for Sasuke. It shows how her experiences, like dealing with the fall of Sakura leaves in the village, symbolize her changing relationship with Sasuke. Another one focuses on Sasuke's return to the village and how Sakura, with the reminder of the sakura leaves (a symbol of new beginnings in their village), tries to reconnect with him on a deeper level.
The theme of hope is quite prominent. The sakura leaves, which are associated with new life and beauty in the Naruto universe, can represent the hope that Sakura has for a future with Sasuke. Also, the theme of sacrifice is there. Sometimes Sasuke's actions for the greater good might seem like a sacrifice of his relationship with Sakura, and the sakura leaves can be a melancholic reminder of what could have been.