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.
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.
One possible storyline could be in a dark AU (Alternate Universe). Maybe there's a powerful new enemy that targets Hinata specifically because of her connection to Naruto. This enemy could have some sort of vendetta against the Hyuga clan and sees Hinata as the key to their downfall. Naruto is then left to deal with the grief and also find a way to avenge her death, which could lead to a whole new arc of him exploring darker powers or making some difficult moral choices.
Well, in this fanfiction, an ending might be that Hinata, in her grief, leaves the village for a while to find herself. When she returns, she has become stronger and more confident. She then devotes her life to making the village a better place, just as Naruto would have wanted. Another ending could be that the whole village unites even more tightly after Naruto's death, with Hinata at the forefront of this unity, as she was the last person Naruto protected.
A common scenario in such fanfictions is that Hinata sacrifices herself in a war - torn situation. For instance, in a great ninja war, Naruto is the key to victory but is targeted by the enemy's most powerful forces. Hinata, with her unwavering love for Naruto, jumps in front of a massive attack aimed at Naruto, knowing full well that it will cost her life. This selfless act then serves as a major turning point in the story, inspiring Naruto and his comrades to fight even harder.
He would feel a deep sense of guilt, thinking that if he had been stronger or more aware, he could have saved her. Naruto might also start to cherish the memories he had with Hinata more, and this could change his personality a bit, making him more somber at times. He would probably vow to protect the things that Hinata held dear, like her family and the village.
Hinata would probably be angry too. She might be angry at the circumstances that led to Naruto's death, whether it was an enemy or some other misfortune. She could direct her anger towards training harder, vowing to become stronger so that she can prevent such a tragedy from happening to others in the future.
One consequence could be Hinata's complete emotional breakdown. She has always been in love with Naruto. His death would shatter her world. She might become withdrawn and lose her will to fight. In the Naruto universe, she is a strong - willed kunoichi, but this event could change her entirely. She could also vow revenge if Naruto's death was due to an enemy, and this could lead her on a dark and dangerous path of seeking vengeance.
In such a fanfiction, one possible plot development could be that Naruto sacrifices himself during a major battle against an extremely powerful enemy. Maybe an enemy that has the power to destroy the entire Hidden Leaf Village. Naruto, being the hero he is, steps in to protect Hinata and in the process, takes a fatal blow meant for her. This would lead to great sorrow among the villagers, especially Hinata who would be heartbroken. She might then vow to carry on Naruto's will and protect the village in his memory.