One way could be that Naruto has been in a time - loop for a thousand years. He keeps reliving certain events, trying to change the outcome each time. For example, he might be trying to prevent a great war that keeps happening no matter what he does in each loop.
One possible development is that Naruto becomes a wise and somewhat jaded mentor. He's seen so much over the centuries that he might be a bit cynical at times, but still has that core of kindness. He could guide the new generation with his vast knowledge.
Yes, there might be such fanfictions. Many fanfic writers like to explore different timelines and scenarios for their favorite characters. In a 'naruto is an old man' fanfic, Naruto could be having adventures that are different from his youth, perhaps mentoring the new generation with his years of wisdom.
One possible fanfiction could be about Naruto at 17 finally getting to know more about his mother Kushina through some kind of time - travel or spiritual encounter. Maybe he discovers some hidden jutsu she created and uses it to defeat a new enemy in the village.
One aspect of such a fanfiction could be the daughter's journey to find her own identity. With Naruto as her father, there's a lot of pressure and expectation. She might struggle to carve out her own path, different from what Naruto has done. And Naruto, as a father, has to learn to let her make her own mistakes and grow. They could have adventures together that help her in this self - discovery process.
I'm not sure specifically as there could be many different takes in a fanfiction with that title. It might be about Naruto in a very different time period, perhaps exploring his character in an ancient or far - future setting.
He might have the power of foresight. Since he has lived for a thousand years, he could predict future events based on his past experiences. For instance, he could foresee an attack from an unknown enemy before it even happens.
Maybe some of the younger ninjas from other villages that he has inspired. For example, a young ninja from the Sand Village who saw Naruto's heroics during the Fourth Great Ninja War and now wants to join him in his quests. They could bring new skills and perspectives from their own village's ninja techniques.
He could be on a mission to protect the Hidden Leaf from a new and powerful enemy. Maybe he has to travel to far - off lands and use his enhanced skills, like his Rasengan, in new and creative ways.
In the plot, it could change the way conflicts are resolved. Instead of relying on brute strength like he might have in his younger days, his hundreds of years of life could make him more diplomatic. He could use his knowledge of past events and different cultures within the Naruto world to broker peace and find solutions that are more long - term and sustainable.