It could be that some of the village elders or leaders send someone to go after her. They might see her running away as a threat to the village's stability or as a potential loss of a valuable asset. Maybe they send a team of ANBU to track her down and bring her back, whether by force or persuasion.
Shikamaru might be sent to find Naruto. He's known for his intelligence and strategic thinking. The village elders might trust him to be able to track Naruto down and either convince him to come back or at least find out his intentions. Shikamaru also has a certain respect for Naruto and would understand his motives to some extent.
Well, perhaps the fanfic could be about Sakura being in an unhappy marriage. She might have discovered some dark secrets about her spouse, like they were involved in illegal activities. So, in order to protect herself or her loved ones, she decides to run away. Maybe she has a secret plan to expose her spouse's deeds from afar.
Kakashi could be another one. As Naruto's former sensei, he knows Naruto's capabilities and potential. He would try to stop Naruto from running away because he believes that Naruto has a future in Konoha and running away isn't the solution to whatever problems Naruto is facing.
Another reason could be for the sake of protecting the village. Maybe he discovers some sort of threat that he believes he can only face by leaving Konoha. He doesn't want the village to be in danger because of him, so he runs away to draw the danger away from Konoha.
Perhaps she is being chased by some unknown enemies in Konoha who are after her for some reason. She might think that running away from Konoha is the only way to protect herself and those she cares about. It could also be that she has a new mission or purpose that she believes can only be achieved outside of Konoha, and she is willing to sacrifice her life in the village for it.
He could run to the Land of Waves. He has a connection there from his early mission. The people there were friendly to him, and he might find some peace and acceptance among them. It's a place where he could start anew, away from the chaos of Konoha.
One possible reason could be feeling ostracized. In the Naruto world, being different is often not easily accepted. As a female Naruto, she might face even more scrutiny and prejudice. Maybe she's tired of the constant expectations and the way she's treated in Konoha, so she decides to run away to find a place where she can be herself.
Sakura would likely become more independent. Running away from a marriage forces her to rely on herself. She would start to make her own decisions without depending on her spouse. For instance, she would have to figure out how to earn money, find shelter, and protect herself.
He could go to the mountains. There are so many hidden caves and areas in the mountains that he could explore. It would be a great place for him to hide and be alone with his thoughts. Plus, there might be some powerful Pokémon that live there that he could interact with.
He could go to the Forbidden Forest. It's a large and mysterious place where he could hide. There are many hiding spots and magical creatures that could either protect him or at least keep his presence a secret.