Maybe Naruto is put in a situation where he feels that Hiruzen's way of handling things is the best option. For instance, if there is a major crisis in the village that requires a more traditional and experienced approach, Naruto might choose to act like Hiruzen. Also, he could be influenced by the stories he has heard about Hiruzen and wants to fill his shoes in a way.
One possible scenario in a 'Naruto Saves Hiruzen' fanfic could be that Naruto uses his newfound powers. Maybe he has mastered a new jutsu that allows him to turn back time briefly. He then uses this power to go back to the moment when Hiruzen is in danger. Naruto's quick thinking and his never - give - up attitude would be highlighted in such a fanfic.
Perhaps Naruto discovers a prophecy that Hiruzen will be in danger. So, he starts to train extra hard to be able to face whatever threat is coming. When the time comes, he uses his speed, which he has enhanced through rigorous training, to reach Hiruzen before the enemy can land a final blow.
Perhaps in this fanfiction, Naruto has some sort of special power or transformation that he unlocks just in time to face Orochimaru. It could be related to his Nine - Tails chakra in a new and unique way. He uses this power to break through Orochimaru's defenses and save Hiruzen. Naruto might also use his knowledge of Orochimaru's weaknesses that he has learned either from Jiraiya or from his own past encounters with Orochimaru's minions.
There are quite a few. One such fanfic is 'The Mentor's Wisdom' where Hiruzen imparts his knowledge and skills to Naruto in a detailed and engaging way.
In the fanfiction, Hiruzen might raise Naruto properly by providing a stable living environment. He could ensure Naruto has a decent place to live, enough food to eat, and warm clothes. This basic care is fundamental for Naruto's growth.
One interesting story could be about Hiruzen mentoring Naruto in some unique jutsu that was long forgotten. This would show a different side of their relationship, focusing on the transfer of knowledge from the old to the new generation.
Perhaps Hiruzen is being influenced by some dark force or a hidden group within the village. They convince him that Naruto, with the Nine - Tails inside him, is too dangerous to be left unchecked. So, Hiruzen, in a moment of weakness, decides to betray Naruto. He could secretly arrange for Naruto to be sent on dangerous missions alone with the intention of getting him killed. Naruto, being oblivious to this at first, later realizes what's going on and has to fight not only against external enemies but also against the betrayal of his own village leader.
In this fanfiction, perhaps Hiruzen realizes Naruto's potential much earlier and decides to train him privately. He might take Naruto on secret missions to build his experience and confidence. This would not only strengthen Naruto's skills but also their bond, which could have a huge impact on the village's future.
Some fans create 'naruto hiruzen bashing fanfic' because they feel Hiruzen made some big mistakes. For example, his handling of the Uchiha clan issue. He knew about the growing unrest but didn't take effective steps to prevent the tragedy. So fans write to show their dissatisfaction with his leadership in such matters.