A scenario could be when Naruto is about to lose control of the Nine - Tails' chakra. Jiraiya, having trained with the Toads who have knowledge about taming the tailed beasts, could use some special sealing techniques or calming methods to prevent Naruto from going berserk. This not only saves Naruto from harming himself but also from potentially causing destruction to his village and friends.
There are quite a few scenarios. For instance, if Naruto were to be targeted by a powerful organization that wants to steal the Nine - Tails' power from him. Jiraiya could step in and fight off the attackers, using his Sage Mode. He might also use his connections in the ninja world to gather allies to protect Naruto. Or, say Naruto is lost in a dangerous, unknown territory. Jiraiya, who has traveled far and wide, could use his experience to find Naruto and lead him to safety.
One scenario could be that Naruto is poisoned during a battle. Jiraiya, with his vast knowledge of herbs and medicine, finds an antidote in time to save Naruto. Another possibility is that Naruto is trapped in a genjutsu created by a powerful enemy, and Jiraiya uses his own genjutsu - breaking skills to free Naruto.
In some fanfictions, Naruto might team up with other unexpected characters. Say, he teams up with some of the Akatsuki members who have a vendetta against Pein for some reason. Together, they are able to save Jiraiya from Pein's clutches.
One possible scenario is that Naruto arrives in the Fairy Tail world just as a powerful dark guild is about to destroy Fairy Tail. He uses his speed and combat skills to take on the leaders of the dark guild and defeats them. Another scenario could be that Fairy Tail is facing a magical disaster, like a powerful spell gone wrong. Naruto, with his ability to adapt quickly, figures out a way to counter the spell using his own ninja powers.
In some fanfictions, Naruto might save a civilian who has been poisoned. He would use his knowledge of herbs and medical ninjutsu to find an antidote and save the civilian's life. There could also be a situation where a civilian is trapped in a burning building. Naruto would brave the fire, using his chakra to protect himself, and carry the civilian to safety. And sometimes, a civilian is being mind - controlled by an enemy, and Naruto has to break the control and save the civilian.
Maybe in the fanfiction, the situation is more complex. Hinata is being held hostage by the Cloud in a heavily guarded location. Naruto infiltrates the place secretly. He uses his transformation jutsu to disguise himself as a Cloud ninja at first to get closer. Then, he reveals himself and uses his Sage Mode to take on all the guards. He finally rescues Hinata and they escape together.
Perhaps Naruto has some sort of premonition about Sasuke's danger. He follows his gut feeling and finds Sasuke trapped by Haku. He then uses his Uzumaki bloodline power, something that might be enhanced in fanfiction, to disrupt Haku's chakra flow and save Sasuke.
One possible scenario could be that the Anbu arrives just in time as Anko is about to use a dangerous jutsu on Naruto. The Anbu might use their superior speed and stealth to disarm Anko and rescue Naruto. Another scenario could be that the Anbu has been secretly observing Anko's actions towards Naruto, suspecting her of having some malicious intent. So they step in when they see Anko cornering Naruto. Maybe the Anbu uses some special ninjutsu to create a diversion and then whisks Naruto away to safety.
One possible scenario is that Hinata and her team are on a mission in an unknown territory. They encounter a group of rogue ninjas. Hinata tries to defend her team but is outnumbered. Just as they are about to be defeated, Naruto shows up, having followed Hinata's chakra signature. He quickly takes down the rogues with his speed and strength.
One possible scenario could be that Naruto leaves to train in isolation. He might feel that he needs to become stronger on his own without the guidance of Jiraiya, and so he sets off to find new ways to improve his skills.
One possible scenario is that Naruto arrives at the Tower of Heaven just in time. Erza could be on the verge of being defeated by a powerful villain. Naruto uses his chakra to boost his speed and punches the villain away. He then quickly takes Erza and flees the tower. Another scenario could be that Naruto has to solve some puzzles or overcome traps in the tower to reach Erza. Once he does, he uses his chakra cloak to protect them both from any incoming attacks as they escape.
One common plotline is Naruto arriving just in time to prevent Jiraiya from being fatally injured by Pain. He could use his newfound powers, like Sage Mode or even some advanced Rasengan variations. Another plotline might involve Naruto using his connection with the Nine - Tails to somehow sense Jiraiya's distress across great distances and rush to his aid. In some fanfictions, Naruto might also enlist the help of his friends like Kakashi or Sakura to form a rescue team for Jiraiya.