Most likely not. Fanfics with such themes are often inappropriate and violate the general ethics and norms of the Naruto series. The Naruto series is mainly about friendship, growth, and ninja adventures, not such improper content.
One possible plot could be a dark turn in the story. Maybe Kakashi is under some kind of mind - control. He could be forced to fight Naruto by a powerful enemy who has taken over his mind. Naruto, being unprepared for such an attack from his mentor, gets killed. This would then lead to a series of events like Sasuke going on a rampage to find out the truth and avenge Naruto, and the whole ninja world being in shock as one of their most promising heroes is gone.
A better fanfic idea could be about Naruko and her training journey to become a powerful ninja. For example, she could go on a special mission with her friends to explore a new and dangerous land, and during this journey, they face various challenges and learn new jutsus.
Often, Gai is paired with Kakashi in Hurt Kakashi fanfiction. Gai, with his unwavering belief in friendship and his eternal rivalry with Kakashi, can be a great character to interact with a hurt Kakashi. He might try to pull Kakashi out of his slump through their friendly competition. Also, Rin is sometimes included. Since she has a significant past with Kakashi, her presence in the fanfiction can either be a source of comfort or more pain, depending on how the story is written.
Naruto is often a common character. Since Naruto has a strong bond with Kakashi, he might be involved in Kakashi's time - traveling adventures. Sasuke could also be there. Their relationship with Kakashi in the original story makes it likely for them to show up. And of course, Guy would be a great addition. His friendly rivalry with Kakashi would add some humor and action to the time - travel scenarios.
Kakashi would likely still maintain his cool and mysterious demeanor. He'd be the experienced ninja, quick to analyze situations and offer sage advice. For example, when faced with a difficult opponent, he'd be calm and strategize on the spot. Hinata, on the other hand, would be her shy yet determined self. She might blush a lot around Kakashi at first but would show great courage when it comes to protecting others. Her Byakugan would be a crucial asset in the story, like if they were searching for something hidden in a lemon grove, she could use it to detect any hidden threats.
Well, often in Hurt Kakashi fanfiction, there's the theme of his physical injuries and how he copes with them. Given his dangerous line of work as a ninja, he gets hurt a lot. Writers might explore how he deals with long - term or serious injuries that could potentially end his ninja career. Also, his relationships can be a source of pain. For instance, his complex relationship with Obito and how that affects his mental state when they are at odds.
Kakashi would become more nurturing. In the original, he was a teacher, but as an adoptive father, he'd have to be more affectionate. He might show his face more often to Naruto, as a sign of trust, and be more open about his emotions.
Rather than a'sexy story', we can recall how Kakashi was always there for his comrades. He faced powerful enemies bravely. His Sharingan - related abilities made him a formidable ninja. His story is more about friendship, loyalty, and the pursuit of peace in the ninja world.