Kakashi's reaction would be complex. He is a man who has lost many people in his life. But Naruto was special. He would hold Naruto tightly, his hands trembling slightly. He might try to use some of his own chakra to keep Naruto alive a little longer, but deep down he knows it's futile. His face would show a mixture of pain, regret, and love. He would remember all the times he trained Naruto, all the lessons he taught him, and how Naruto had surpassed all expectations.
A theme that often comes up is his physical pain and how he endures it. This can be used to show his strength and tenacity. For example, in a battle - themed fanfiction, he endures great pain but still manages to fight for the sake of his village. Also, the theme of self - discovery through pain is common. As he experiences pain, he learns more about himself and his limits.
I'm not sure specifically as there could be many different takes in a fanfic with that title. It might be about a character in Naruto who endures some sort of unending pain, perhaps related to their past traumas, like Naruto himself who has the pain of being an orphan and ostracized for so long. Or it could be about a villain like Sasuke who has his own internal pain that never seems to go away.
One idea could be that Rin, with her medical skills, tries to save Kakashi but fails due to some unforeseen circumstances. Maybe an enemy uses a powerful jutsu that she can't counter in time. This would be a tragic twist, as her being alive doesn't change the outcome for Kakashi.
Since I haven't read it, I can't say for sure. But it could be Naruto, as he is the main character of the original series and has a lot of pain in his past. It might also focus on Sasuke, who has his own set of traumas and pain related to his family and his quest for revenge.
The theme of sacrifice could also be present. Both characters are willing to sacrifice for their causes. In the context of a yaoi fanfiction, this could translate into sacrifices for each other. For example, Pain might sacrifice his original plans for world domination for Kakashi, or Kakashi might put his village - related duties on hold to be with Pain, exploring the lengths they would go for their relationship.
Another possible fanfiction could be centered around Kakashi's pain from his past traumas, like the loss of his father. It could show how these past experiences resurface when he faces a new threat in the village. The story could detail how he overcomes this pain by finally coming to terms with his past and using it as a source of strength.
One possible plotline could be that Kakashi is in a life - threatening situation during a battle against a powerful enemy. Naruto, seeing no other way to save him, uses a powerful and self - sacrificing jutsu that costs him his life. Another plotline might involve Naruto making a deal with some dark force to save Kakashi, but the price is his own life. Or perhaps in a mission gone wrong, Naruto takes a fatal blow meant for Kakashi.
In such a fanfiction, the emotional impact would be huge. Naruto is a central character, and his sacrifice for Kakashi would shock the Naruto universe. It would leave characters like Sasuke, Sakura, and the entire Hidden Leaf in mourning. Kakashi, who has always been a mentor to Naruto, would likely be consumed by guilt and a sense of unworthiness. The story could explore themes of self - sacrifice, loyalty, and the bonds between teacher and student on a very deep level.
I'm not sure of a specific 'naruto dies saving kakashi fanfiction' off - hand. You could try searching on fanfiction - dedicated websites like Archive of Our Own or FanFiction.net.