In some fanfictions, Naruto might get injured by Nagato's powerful jutsus. For example, Nagato could use his Chibaku Tensei in a more unexpected way, catching Naruto off - guard and causing him physical harm. Maybe Naruto tries to approach Nagato too quickly to reason with him and Nagato, in a split - second decision, uses a blast of Shinra Tensei to push Naruto back, resulting in Naruto getting injured as he crashes into surrounding debris.
In some fanfictions, Naruto might get the Rinnegan from Nagato through a transfer of power. This could be due to Nagato seeing Naruto as a worthy successor and using some sort of jutsu to pass on the Rinnegan's power before he dies. Another possibility is that there is some sort of magical or spiritual connection between them that enables the transfer.
One consequence could be that it makes Naruto more cautious. He might start to reevaluate his approach to Nagato and their conflict. Another consequence could be that his friends and allies become more worried and protective. For example, Sakura might rush to his side to heal his injuries, and Kakashi could start formulating a new strategy to deal with Nagato while Naruto is recovering.
One possibility is that there was some sort of spiritual or chakra - based connection between Naruto and Nagato. Nagato, being the possessor of the Rinnegan, recognized Naruto's strong will and the fact that he was on a path to change the ninja world for the better. Through this connection, Nagato was able to transfer the power of the Rinnegan to Naruto. It could also be related to the nature of the Sage of Six Paths' power that was somehow involved in this transfer, as both Naruto and Nagato were related to the Sage in different ways.
It might be that he was trying to protect some of the Fairy Tail guild members from a dangerous enemy. In the process, he took on more damage than he could handle. For example, if a powerful demon was attacking the guild, Naruto might jump in front of it to save his newfound friends, getting seriously injured in the process.
In these fanfics, Nagato may help Naruto on an ideological level. Nagato once believed in a very different way of achieving peace. By sharing his journey and how he came to realize the flaws in his thinking, he can guide Naruto in his pursuit of true peace. Nagato could also use his influence over the Akatsuki remnants to prevent them from causing more chaos, which in turn helps Naruto in his mission to protect the ninja world.
It's also possible that he gets injured while trying to save someone. Sam is known for his selfless nature. He could be rushing to protect an innocent bystander from a supernatural creature, like a werewolf or a vampire, and in the process, get bitten or scratched, which would lead to an injury.
In some fanfictions, Naruto and Nagato might be related through their shared experiences with the ninja world. They both faced great tragedies. Naruto could be seen as a successor to Nagato's ideals in a way. Nagato once wanted peace through force, but Naruto shows that peace can be achieved through understanding and forgiveness.
The Rinnegan would supercharge Naruto's abilities. Naruto already has a vast amount of chakra and with the Rinnegan, he could use that chakra in more diverse and powerful ways. He might gain the ability to use the Deva Path's power to manipulate gravity, which could be used both defensively and offensively. His Sage Mode combined with the Rinnegan could create a whole new level of fighting style, allowing him to quickly assess and counter his enemies' moves more effectively.
Nagato, in fanfiction, can be depicted in various ways. Some may show him as a more conflicted character. He has his own beliefs which were shaped by his experiences, like the death of his friends and the destruction he witnessed. He may be more hesitant to change compared to Naruto, but also has the potential for redemption which makes his character interesting.
When trained by Nagato in fanfiction, Naruto's character development would likely involve a growth in his understanding of power. Nagato has a different approach to power compared to Naruto. Through Nagato's training, Naruto may learn that power isn't just about physical strength but also about knowledge and the ability to make tough decisions. This could add a new layer of maturity to Naruto's character.