Well, in a fanfiction where Naruto is executed by family, the entire Naruto universe would be drastically changed. Firstly, Naruto was the Jinchuriki of the Nine - Tails, so his death would mean the Nine - Tails would need to be dealt with in some way. This could potentially lead to it going on a rampage or being sealed in a different way. Secondly, the bonds that Naruto had formed with so many characters would be shattered. His friends like Sasuke, Sakura, and Kakashi would be deeply affected. They might turn bitter or vengeful. The village of Konoha would lose one of its greatest protectors. This could lead to a decline in the village's prosperity and safety. The story could also show how the family that executed Naruto would be ostracized by the rest of the village and how they would try to redeem themselves or face the consequences of their actions.
The balance of power would be severely disrupted. Naruto was a key figure in maintaining peace. His execution by family would create chaos as his friends and allies would be in shock and seek justice. Villages that were in alliance with Konoha might question the stability of the village. Also, the younger generation that looked up to Naruto would lose their inspiration.