Yes, there are such fanfictions in the Naruto fanfiction community. Some fans like to explore unique and creative scenarios in their writing, including this rather unexpected one.
In the 'naruto is protected by sasuke fanfiction', Sasuke's protection of Naruto could be multi - faceted. Sasuke, being a powerful ninja, would first of all use his physical strength and speed to block attacks aimed at Naruto. Emotionally, his bond with Naruto would make him extremely vigilant. He might sense Naruto's distress from afar and rush to his aid. In terms of strategy, Sasuke would likely plan their movements carefully when they are in dangerous situations, ensuring Naruto is always in a relatively safe position. His ability to quickly analyze a battle situation and react accordingly would be crucial in protecting Naruto.
Well, in some fanfictions, Naruto might be promoted over Sasuke because Naruto has always been seen as the more positive and inspiring character. He has a strong will to protect his friends and the village, and his growth throughout the series is more in line with the traditional hero's journey. His ability to make friends and bring people together could be a reason for his promotion in the fanfiction.
It might be for Naruto's own good. Sasuke may believe that Naruto is on a dangerous path that will lead to his downfall. So he captures him to keep him from making bad decisions, like sacrificing himself for the village or something similar. He wants to save Naruto from himself in a sense.
In some fanfictions, Naruto might reject Sasuke because of Sasuke's continuous pursuit of power in a way that endangers others. Naruto, who values friendship and the safety of the village, could see this as a betrayal of their shared values.
Naruto might protect Sasuke by using his physical strength. He's got those powerful jutsus like the Rasengan. If any enemy comes near Sasuke, Naruto can just blast them away with his attacks.
I don't think it's a common type. The typical Naruto fanfictions usually revolve around things like the ninja battles, the growth of the characters, or the complex relationships in a more traditional sense. The concept of one character being the 'property' of another is a bit extreme and not in line with the general feel of the Naruto series. So, it's not likely to be a very common form of fanfiction.
One popular theme is the growth of their individual powers. Writers like to explore how Sasuke and Naruto further develop their abilities, such as new jutsu or enhanced forms of their existing powers. This keeps the action and excitement going in the fanfiction.
One possible fanfiction scenario could be that Hinata, Sasuke and Naruto are on a difficult mission together. They start off with some tension due to Sasuke's past actions. However, as the mission progresses, they learn to trust each other more. Hinata might use her gentle nature to ease the situation between Naruto and Sasuke. Naruto's determination and Sasuke's skills combine with Hinata's support to make them a formidable team in this fictional adventure.
One popular place to search for Sasuke x Naruto fanfiction is Archive of Our Own (AO3). There are tons of well - written stories there that explore different aspects of their relationship, from friendship - based ones with a lot of angst to more romantic interpretations. Another option could be FanFiction.net, which also has a large collection of fan - created stories about these two characters.