Simple. Naruto is Kurama's jinchuriki. In fanfiction, just like in the original story, they share a special bond. Kurama doesn't want his host to die because it would mean his own end too.
In some fanfictions, Kurama becomes protective when Naruto is wrongly accused by the village again. Kurama provides Naruto with extra strength and wisdom to face the situation. He might even communicate with Naruto more directly than in the original series, sharing his ancient knowledge to help Naruto clear his name.
The Kurama Brothers could be entities that have a similar origin to Kurama. They might have been part of the same chakra - based creation in the Naruto universe. They could possess some of Kurama's traits like great power and a connection to the natural energy in the world. They are often depicted as having their own personalities, with one being more hot - headed and the other more calm and calculating. Their relationship with Naruto usually involves them using their powers and knowledge to help Naruto grow as a ninja and a person. They might also have their own goals and motives that are intertwined with Naruto's journey.
Well, Kurama might train Naruto by teaching him how to better control and access chakra. Since Kurama has a vast amount of chakra, it could show Naruto unique ways to harness and use it. For example, it could guide Naruto in creating more powerful and complex jutsu by using their combined chakra in a more efficient way.
Kurama might become angry at first. He's a powerful being and being neglected would likely wound his pride. He could start causing some minor disruptions inside Naruto, like making it harder for Naruto to access his chakra.
One reason could be that he sees Naruto as a younger version of himself in some ways. Both have had their share of loneliness and challenges growing up. Kakashi may want to prevent Naruto from going through the same pain he did. Another reason is Naruto's importance to the village. As the jinchuriki of the Nine - Tails, Naruto is a key asset. Kakashi, being a loyal ninja, wants to protect the village's future which is tied to Naruto.
Well, Naruto has a huge and passionate fan base. People are protective of Naruto fanfiction because it's a way to keep the Naruto universe alive. It allows fans to explore different storylines, relationships, and character developments that they might have imagined while watching or reading the original Naruto. It's like a creative extension of the beloved series.
Well, Rookie might protect Naruto by always being by his side during dangerous missions. For example, when facing strong enemies, Rookie could use his own skills to shield Naruto from attacks.
It might be portrayed as a very strong and almost spiritual connection. They could be shown as two halves of a whole, with Naruto relying on Kurama not just for power but also for emotional support and vice versa.