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.
A possible plot could be that Kakashi sacrifices himself to save Rin from a powerful enemy. This would be ironic as usually, Kakashi is the one protecting others. With Kakashi gone, Rin might then discover some secrets that Kakashi was keeping from her. These secrets could change her view of him and also drive the rest of the fanfiction as she tries to come to terms with his death and the new information.
Kakashi is known for his laid - back yet highly skilled nature. His influence on Naruto could be in terms of teaching him to be more strategic in battles. Rin, being kind - hearted and having a strong sense of care, would give Naruto the emotional support he lacks. So Naruto might become more balanced in his approach to life and ninja - hood.
In a fanfiction of Kakashi and Rin's love story, it could start with their time in the ninja academy. Rin was always drawn to Kakashi's natural talent and mysterious aura. Kakashi, on the other hand, was initially oblivious to Rin's feelings. One day, Rin got injured during a training session. Kakashi carried her all the way to the medical tent. That was the first time he realized how much she meant to him. As they grew older, their bond deepened, and they found themselves falling in love while on various missions.
There are indeed such fanfictions. In these stories, Rin's survival can have a huge impact on the other characters. For example, it could change Obito's path completely. Instead of becoming consumed by hatred, he might have a different future with Rin alive. Also, Kakashi's character development could take a different turn as well, since Rin was an important part of his past.
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.
Growth is also a common theme. The family members, whether it's Kakashi, Rin or their kids, usually experience personal growth throughout the story. They learn from their experiences, overcome difficulties, and become better versions of themselves as a family.
Yes, there are quite a few. You can check out some popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'kakashi and rin married' in their search bars, and you'll likely find some interesting stories.
One popular one might be 'The Unspoken Bond' which delves deep into their relationship in a rather emotional way. It shows how Kakashi and Rin's bond could have developed over time.