Most of the fandom would probably be horrified. Naruto is known for his positive values, and killing a family member is completely against that. There would likely be a lot of criticism towards the author of such a fanfic.
I'm not sure if there is an actual 'naruto kills his sister fanfic' specifically. But if there were, it would be a very twisted take on the Naruto universe. Naruto has always been shown to value family, even if he didn't have a traditional family growing up. He found family in his friends and in the village. So this idea of him killing his sister would be a radical departure from his core values.
If such a fanfiction exists, one possible reason could be a mind - control situation. Maybe an enemy uses some powerful genjutsu to make Naruto believe his sister is a threat, causing him to kill her accidentally. Another reason could be a misinformation plot where Naruto is tricked into thinking his sister has committed some unforgivable crime against the village.
I'm not aware of any official 'Naruto kills his sister' fanfiction. This goes against the general nature of Naruto's character who values family and friends. Fanfiction that involves such extreme and out - of - character scenarios might be very rare or non - existent in the mainstream Naruto fanfic community.
At first, Sasuke might not believe it was Naruto's own will. He would try to find out if Naruto was under some sort of external influence. But if he found out that Naruto was fully responsible, Sasuke's reaction would be one of pure hatred. He would abandon all his previous beliefs and goals and make it his sole mission to destroy Naruto. He might also cut off all ties with the village that Naruto was protecting, seeing it as an accomplice in his sister's death.
He could be feared by the remaining ninja. Since he has killed all his enemies, others might see him as a ruthless killer rather than a hero. This could lead to isolation as people would be scared to approach him.
Naruto would use his ninja skills. He might start with a diversion, like creating some clones to distract the assassin while he gets his sister to a safer place.
It could be an original character created just for the fanfiction. Many fanfiction writers like to introduce new characters to add their own unique twists to the story.
I'm not sure if there is such a specific fanfic. Fanfics cover a wide range of themes, but abuse within family in a Naruto fanfic might be a rather dark and not - so - common take. It could exist in some corners of the vast fanfic community, but it would also be quite controversial as Naruto is generally depicted in positive relationships in the original series.
One possible motive could be jealousy. Maybe she was jealous of Naruto's growing power and popularity within the village. Another reason might be related to some dark family secret or a curse that forces her to take his life against her will.