For Naruto, running away might make him more determined to prove his worth and protect his friends. He could learn to control his Nine - Tails chakra better in the face of danger outside the village. Sasuke may start to trust Naruto and Sakura more, realizing that they are his true comrades. Sakura, on the other hand, could become more independent and confident in her abilities, not just relying on Sasuke and Naruto but also being able to take charge when needed.
One possible plot could be that they run away from the Hidden Leaf Village to avoid a powerful enemy that is targeting them specifically. Maybe this enemy has some vendetta against them because of their unique abilities or past actions. They might have to rely on each other's skills and their friendship to survive in the wild and find a new place to call home.
Their relationship could develop into a deeper friendship. Away from the daily hustle and bustle of the village, they would rely more on each other. Naruto would see Sakura in a new light, not just as a teammate but as a true partner. And Sakura would appreciate Naruto's unwavering loyalty more than ever.
A plot could be that they are being hunted by a powerful and evil ninja organization. So they run away to gather strength and allies. Naruto might try to convince some of his old friends from other villages to join their cause. Sakura would be constantly worried about their safety but also determined to fight back.
Well, they could embark on a journey to discover a hidden ninja village that holds the key to a powerful jutsu. Along the way, they might face various challenges like traps set by rival ninja clans. And Naruto would probably be the one to keep everyone's spirits up with his positive attitude.
A simple reason could be to escape a dangerous prophecy. Maybe there's a prediction that they will cause great harm to the village if they stay, so they run away to figure out how to change their fates.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.