In some fanfictions, it could be due to a special jutsu gone wrong. Maybe a jutsu that Kakashi was using to transfer some of his chakra to Naruto for a mission accidentally transferred his Sharingan power as well.
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.
Another possibility is that Sakura would feel really down at first. But then, inspired by her love for Sasuke or her desire to protect her friends, she would pull herself together. She could approach other more approachable senior ninjas for advice on how to train without Kakashi's guidance. For example, she might go to Shizune, who could give her some basic medical - ninjutsu training tips that she could build on herself. And she could also practice her physical strength training on her own, like doing extra push - ups and running drills in the forest.
One way could be through words of wisdom. Kakashi has a lot of life experience and could share his insights with Sasuke, like how to deal with his inner turmoil and the path he should choose. For example, he might tell Sasuke that revenge isn't always the answer and that there are other ways to find peace.
The moment when Kakashi actually reaches Naruto and stops him from harming himself is crucial. He could use his speed and strength to grab Naruto's hands if he was about to use a weapon on himself. Kakashi's presence alone at that moment can be a shock to Naruto, making him pause and re - consider.
Well, Kakashi might use his Sharingan to intimidate the civilians and create an opening to grab Naruto. His quick jutsu skills could also be a factor, like using a clone to distract the civilians while he gets Naruto to safety.
He might learn some advanced chakra control techniques. For example, better management of his Nine - Tails chakra. Kakashi, being a skilled ninja, could teach Naruto how to blend his own chakra with the Nine - Tails' more effectively, which would enhance his combat abilities.
Regular Kakashi and Sakura fanfiction usually focuses on their relationship in a more general sense, like friendship or mentorship. But 'hard lemon' fanfiction (if we assume it's not inappropriate) might explore more intense emotions or situations between them, perhaps more romantic or even angsty scenarios that are not typically explored in the regular ones.
Kakashi would probably focus more on stealth training. In the original, Naruto was more about big, flashy attacks. But Kakashi would teach Naruto how to move quietly and strike unexpectedly. He might also teach Naruto more about chakra control from the very beginning. In the original, Naruto struggled with this for a while. And Kakashi would surely introduce Naruto to some of his own unique jutsu earlier, like the Chidori, but with Naruto's own spin on it.
Naruto might also try to find alternative ways to gain strength. He could explore the forest around the village to find new training areas or discover new chakra - related phenomena. He has a curious nature, and this could lead him to stumble upon something that gives him an edge in his training, like a hidden hot spring that has special chakra - enhancing properties.