It's not extremely common, but there are some out there. One example might be some darker, alternate universe fanfics where the author wants to explore the consequences of Naruto's death on the Hidden Leaf Village and his friends. However, it goes against the main narrative of the original series, so it doesn't have as large of a following as more positive or canon - compliant fanfics.
These types of fanfictions can be quite interesting in their own way. They might explore different aspects such as how the power balance in the ninja world shifts. Maybe villains become more dominant without Naruto there to oppose them. However, many fans who love Naruto for his positive, underdog - to - hero story may not be as drawn to these darker fanfics where he is killed in action. It really depends on the reader's taste for exploring alternative, often more tragic scenarios in the Naruto universe.
It's a rather unique concept. In the original Naruto series, Kakashi is a mentor figure to Naruto. The idea of Kakashi killing Naruto goes against the general bond and narrative. So in fanfiction, it's not a common theme as most fanfics tend to follow the positive relationships from the original. However, it can attract those who like exploring dark or alternative storylines.
One possible plot could be a misunderstanding within Konoha. Maybe some false information is spread about Naruto being a threat. Some radical elements in Konoha then take it upon themselves to eliminate him, believing they are protecting the village.
A possible plotline is that Naruto is killed by a powerful curse placed on him as a child. Maybe it was a curse from a long - forgotten enemy of the Uzumaki clan. His death would cause a chain reaction. Hinata might be so heartbroken that she devotes her life to finding a way to bring him back. Sasuke, on the other hand, could go on a dark path of revenge, believing that Konoha didn't do enough to protect Naruto. And Kakashi would be filled with guilt for not being able to safeguard his student.
One reason could be to explore the darker side of the Naruto universe. Writers might want to see how the characters and the world would react to such a major loss.
One great fanfiction could be 'Naruto's Adorable Adventures'. It might show Naruto in his daily life in Konoha, doing cute things like befriending little animals while on a mission or getting into harmless mischief with his friends. His innocent and positive attitude makes every situation he's in super cute.
One popular Naruto eye bloodline fanfiction could be 'The Uchiha Naruto'. In this, Naruto might gain the Sharingan through some unique plot device. It could explore how he copes with the new power and the secrets that come with the Uchiha bloodline.
It's not that common, really. The main narrative of Naruto is centered around their friendship and rivalry, not one killing the other in a definitive way. Most fanfiction focuses on their growth and development together rather than such a tragic end for Naruto at Sasuke's hands. However, there are a few out there that might explore this for shock value or to create an alternate universe scenario.
One common plotline could be Naruto's friends rallying around him. For example, Sasuke might put aside their differences and visit Naruto while he's sick. He could bring some special herbs or medicine that he found during his travels. Another plotline could involve Naruto having a fever and having strange dreams about his past and future. In these dreams, he might see visions of his parents or get premonitions about threats to the village. And sometimes, the story could focus on how the village itself copes with Naruto being sick. The villagers who once shunned him might now realize his importance and come together to support him in his time of need.
Often, in these fanfictions, Naruto is betrayed by Sasuke again in a different way. Sasuke might side with a new group that has a vendetta against Naruto or Konoha. This could lead to some epic battles where Naruto is not only fighting his former friend but also trying to understand why he has been betrayed. It also gives room for Naruto to grow and develop new powers as he faces this new challenge alone.
Another plotline might involve Naruto's friends betraying him. Suppose Sasuke, out of his thirst for power and a twisted sense of rivalry, teams up with some dark forces against Naruto. This would create a lot of emotional turmoil for Naruto as he has always considered Sasuke a brother.