In such a fanfiction, Naruto could die in various ways. Maybe his sister is somehow possessed and attacks him fatally. Or there could be a situation where she accidentally causes his death during a fight due to a lack of control over her power.
Well, it depends on the specific plot of that fanfiction. It could be that his sister has been turned against him by an enemy. She might use some powerful jutsu that she doesn't fully understand, and it ends up killing Naruto. For example, if she tries to use a space - time ninjutsu to protect Naruto but it backfires and takes his life instead.
There are numerous possibilities. It might be a tragic accident. His sister could be trying to help Naruto in a dangerous situation, like against a powerful enemy. But in the chaos, she makes a wrong move. Maybe she throws a weapon or uses a ninjutsu that hits Naruto instead of the enemy, leading to his death.
In the Naruto series, Naruto doesn't have a biological sister in the original story. So in this fanfiction, the author probably creates a new character to be his sister. It could be an original character with unique abilities and a complex backstory that leads to the situation where Naruto dies by her hand.
There could be a scenario where Naruto sacrifices himself to save Boruto or the entire Hidden Leaf Village from a catastrophic event like a massive attack by an unknown and dangerous force. He might use all his chakra to protect the village, leaving him with no energy to survive.
Well, it could be that his family's secrets or some sort of family curse led to his death. Maybe his family had a connection to a powerful and dangerous enemy who targeted Naruto because of that family link.
In this kind of fanfiction, his sister would probably be devastated. She might go through a long period of grief and could potentially vow to avenge Naruto's death if it was caused by someone.
He would be filled with rage. Naruto has a strong sense of justice and the fact that someone took Hinata away from him would fuel his anger. He would vow to find and punish whoever was responsible. He might even become reckless in his pursuit of vengeance, endangering himself and those around him. His friends would have to step in to try and bring him back to his senses.
Naruto might also try to remember Sakura in a positive way. He would cherish the memories they had together. He could start initiatives in the village in her name, like promoting medical ninja training more, since Sakura was a great medical ninja. He would slowly turn his grief into a force for good in the village.
There's a good chance he would meet Itachi. Itachi had a complex relationship with Naruto and played an important role in the overall story. In heaven, they could clear up any misunderstandings and Itachi could explain his actions more fully to Naruto, and Naruto could perhaps offer his forgiveness and understanding.
The characters in 'Naruto' would be deeply affected if Naruto dies at birth in fanfiction. Jiraiya would be one of the most affected. He saw Naruto as his protege and the hope for the future. Without Naruto, Jiraiya might lose his enthusiasm for training and spreading his teachings. Tsunade would also be saddened as she had a connection to Naruto through her relationship with Jiraiya and Minato. The Rookie 9, Naruto's friends, would have a completely different dynamic. They might not form as tight a group without Naruto's energetic and positive influence. And the Sannin, as a whole, would have their relationships and legacies altered without Naruto in the picture.
He would be filled with a deep sense of grief. Naruto has always cared about Hinata, and her death would be like a part of him has been ripped away. He might isolate himself for a while, blaming himself for not being able to protect her. But eventually, he would use his pain as motivation to get stronger and fight against whatever caused her death.
If Naruto dies at birth in fanfiction, it would have a huge impact on the story's positive themes. Naruto was a symbol of perseverance and the ability to overcome one's past and hardships. His death would mean that those themes would be lost. Also, the Akatsuki's plans regarding the Nine - Tails would be disrupted. They might turn their attention to other 'jinchuriki' more quickly. And characters like Iruka, who played an important role in Naruto's life, would have a completely different story arc as they would not have Naruto to mentor and befriend.