Kakashi might immediately offer a comforting presence. He could put his hand on Naruto's shoulder and just be there silently, letting Naruto know he's not alone.
One possible reason could be that Naruto is feeling lonely. Despite having friends, there are times when his past as an orphan and the years of being shunned by the villagers resurfaces, making him feel isolated. Kakashi finding him in such a state might then lead to a heart - to - heart conversation about Naruto's inner struggles.
One possible fanfiction could be that Kakashi stumbles upon Naruto crying alone in the forest. He sits beside Naruto quietly, not saying a word at first. Then he gently puts his hand on Naruto's shoulder and tells him that it's okay to cry, that showing vulnerability doesn't make him weak. Naruto then pours out his heart about his loneliness and how much he misses his parents. Kakashi listens intently and shares some of his own experiences of loss, creating a deep bond between them in that moment.
Their relationship is like a mentor - mentee bond. Kakashi has trained Naruto, and when he sees Naruto achieve great things, it can be overwhelming. For example, when Naruto masters a new jutsu that Kakashi thought was difficult for him, Kakashi might cry out of joy for Naruto's accomplishment.
Kakashi would likely be very concerned. He would immediately assess Naruto's injuries. If they were serious, he would use his medical skills to start treating him right away. His first reaction would be to make sure Naruto was stable and out of immediate danger.
Well, Kakashi is a complex character. When he discovers Naruto is abused in the fanfiction, he may first feel a deep sense of guilt for not noticing earlier. He'd then use his skills and influence in the village. He could start by reporting it to the proper authorities in Konoha, like the Hokage. And at the same time, he'd be there for Naruto, providing emotional support, talking to him, and helping him through the trauma. Kakashi has his own past traumas, so he'd understand what Naruto is going through on some level.
He'd probably be a mix of angry and sad. Angry at whoever or whatever caused Naruto to be in this state, and sad because he cares about Naruto so much. He might clench his fists tightly, trying to control his emotions while he focuses on helping Naruto. He'd also feel a sense of guilt, wondering if he could have prevented this from happening.
One possible plot could be that Naruto was on a mission alone and got ambushed by a group of rogue ninjas. Kakashi, while out on his own patrol, stumbles upon the injured Naruto. He quickly takes Naruto to a safe place and uses his medical ninjutsu to stabilize him. Then, he might start to investigate who attacked Naruto and why, leading to a revenge - based sub - plot or uncovering a larger conspiracy against Konoha.
Kakashi would probably be very calm at first. He's an experienced ninja who has seen a lot. He'd gently pat Naruto on the back, offering silent comfort. Then he might start to speak softly, asking Naruto what's wrong in a gentle voice.
The plot might involve Naruto crying due to a misunderstanding with his friends. Kakashi witnesses this and steps in to mediate. He first calms Naruto down and then arranges for Naruto and his friends to have an open conversation. During this process, Kakashi shares some wisdom about friendship and communication, helping them resolve their differences.