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.
It could be a rogue Anbu member. This person might be jealous of Naruto's power and popularity within the Anbu. So, they spread false rumors about Naruto which lead to his decision to leave the village. This antagonist would then try to further harm Naruto while he's outside the village, using their own Anbu skills against him.
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.
Naruto might encounter a group of rogue ninjas. At first, they seem like enemies, but as he gets to know them, he realizes they have their own reasons for being outcasts. They could teach Naruto some unorthodox fighting styles that are not taught in the Leaf Village. Also, there could be a mysterious traveler who has knowledge about Naruto's family that even he doesn't know. This traveler could be the key to unlocking some hidden power within Naruto.
Well, Naruto could leave the village in a fanfic due to a prophecy. He might believe that leaving is the only way to fulfill a greater destiny that the village can't support. As he leaves, he starts to explore different cultures of the ninja world. He learns about new forms of jutsu and how other villages operate. He could also form a team with outcasts from different villages, and together they strive to change the way the ninja world views things.
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.
Definitely Naruto and Sasuke. Naruto is the one leaving the village, so he's a central figure. Sasuke, given the 'narusasu' aspect, is bound to play a crucial role too. He could be the one Naruto is leaving behind, or he could be the one who follows Naruto out of the village. There might also be other supporting characters from the Naruto universe like Kakashi or Sakura who could be affected by Naruto's departure.
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.
Perhaps the ANBU has a personal vendetta against someone in Konoha who is too powerful to take on while remaining in the village. Leaving Konoha gives them the freedom to train and gather allies to come back and face their enemy. They might leave secretly, under the guise of a mission, and start building their strength in the outside world, all while Konoha is left in the dark about their true intentions.
In some fanfictions, Naruto might leave the Anbu due to internal conflicts within the organization. There could be corruption or power struggles. Naruto, being the idealistic character he is, would not want to be part of such a messed - up system. He might have discovered some dark secrets about the Anbu that made him decide it was not the place for him.