It can strengthen their relationship. Naruto saving Sasuke shows that he cares about her safety. Sasuke will start to see Naruto as a true friend and protector, which can lead to more trust between them.
Well, it could be that Naruto witnesses Sasuke being bullied, like maybe some villagers are taunting her about her clan. Naruto, being the hero he is, jumps in and scares the bullies away. Then he takes Sasuke to a quiet place and they have a heart - to - heart about how they both feel like outcasts in some ways.
Saving the girl would likely make Naruto more confident in his role as a protector. He would see that his actions have a real impact on others' lives.
Well, Naruto is known for his loyalty to his friends. So he probably steps in between Sakura and the bullies, using his quick thinking. He might make a joke or two to diffuse the situation at first, but if the bullies don't back off, he'll be ready to fight. His Rasengan is a powerful move he could threaten them with if needed.
It might also make Kakashi more protective of Naruto in the future. He realizes how important Naruto is not just to the village but also to him personally. So, he may be more involved in Naruto's training and growth.
Well, in the fanfiction, Naruto could save Ino from Sasuke by appealing to Sasuke's former friendship. Naruto might talk to Sasuke, reminding him of their days in Team 7 and how Ino is also their comrade, which makes Sasuke change his mind and let Ino go.
Well, in the fanfiction, Naruto might use his speed and agility to whisk Sasuke away from the fangirls. Maybe he creates a diversion, like using a clone to draw the fangirls' attention while he grabs Sasuke and flees to a safe place.
In the Naruto saves Karin fanfic, the act of saving Karin by Naruto can have a profound impact on their relationship. Karin has always been on the periphery of Naruto's world, but this event would bring her closer. She may start to believe in Naruto's ideology more strongly. Naruto would also develop a more protective stance towards Karin. This new dynamic could lead to more interactions between them in the future, both in battle and in more personal, emotional situations.
It could make Sasuke more protective of Naruto. Sasuke has always had a complex relationship with Naruto, and seeing him lose an arm would stir up some deep emotions. He might feel guilty, especially if he was somehow involved in the incident that cost Naruto his arm. This could lead to Sasuke staying closer to Naruto and being more open about his feelings.
In fanfiction, the 'hot sauce punch' might be a turning point. It could make Sasuke realize that Naruto still has that goofy side and it might soften his cold exterior. On the other hand, if Naruto uses it out of anger, it could deepen the rift between them. For example, if Sasuke has just made a decision that Naruto strongly opposes, the punch could be a physical manifestation of his frustration.
In some fanfictions, the curse mark can initially drive a wedge between Naruto and Sasuke. Sasuke might become more withdrawn and brooding due to the power and dark influence of the curse mark. Naruto, on the other hand, would be worried about his friend but might not fully understand what Sasuke is going through. This could lead to some misunderstandings and arguments between them as Naruto tries to reach out while Sasuke pushes him away.