The 'broken' theme can be shown through their physical states. Maybe Kakashi has a permanent injury that limits his abilities, and Naruto has some sort of internal chakra imbalance. This makes them feel less than whole. It can also be portrayed in their mental states. For example, Kakashi could be haunted by his past failures even more deeply, and Naruto could be losing faith in his ability to achieve his goals.
In 'broken naruto kakashi fanfiction', the character development can be a key point. For Naruto, perhaps his dreams are shattered in this version, and we see how he copes with that. As for Kakashi, his past traumas could be magnified, affecting his present actions more severely. Also, the plot might revolve around fixing what's broken. It could be about mending their friendship, or restoring the balance in the ninja world that has been disrupted in this fan - created scenario.
Well, there could be. Fanfiction writers love to explore unique and unexpected relationships. Since Naruto and Kakashi are both popular characters in the Naruto universe, some writers might come up with such a plot for the sake of creativity and exploring different storylines. But it's not a part of the official Naruto story.
Sasuke could be a popular character. He might be involved in the story in a way that either helps or hinders the situation where Naruto hurts Kakashi. For example, if Sasuke tries to stop Naruto from doing something stupid that would hurt Kakashi.
Another reason could be related to Kakashi's past actions. If there are some secrets or things Kakashi did in the past that come to light and Naruto doesn't like them, he could snap at Kakashi. Naruto has a strong sense of justice and loyalty, so if he feels betrayed or misled by Kakashi, his reaction could be to snap.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.
One possible reason could be that Kakashi is preoccupied with other important matters in the village. Maybe he has some top - secret missions or tasks assigned by the Hokage that demand his full attention, leaving him with little time to focus on Naruto.
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.
Sakura could also be present. She might be observing the training and learning some things herself, or she could be helping Kakashi in some way, like providing medical support during intense training exercises.
One memorable moment could be when Kakashi finally reveals a powerful new jutsu to Naruto that completely changes the way he approaches battles. Another might be when Kakashi saves Naruto from a near - fatal attack during a tough training session.