It could mean that in the Naruto fanfiction universe, the Kyuubi (Nine - Tailed Fox) has some sort of emotional investment or interest in the stories being written about Naruto. Maybe the fanfictions explore aspects of their relationship in new and interesting ways that the Kyuubi, in the context of these fictional tales, is somehow aware of or involved in.
One way the Kyuubi can show it cares about Naruto fanfiction is by being a consistent and important part of the stories. If the Kyuubi is always there to support Naruto, either by giving him power or by sharing its wisdom, in various fanfiction scenarios, it indicates that it has a role to play and is interested in the development of the fan - created Naruto stories. Fanfiction often plays with the relationship between the two, and if the Kyuubi is actively engaged in these new storylines, it can be seen as caring about the Naruto fanfiction.
One common scenario is when Naruto is in a life - threatening battle. Sakura will be on the sidelines, worried sick and using her medical skills to the fullest to keep Naruto alive. She might even put herself in danger to reach Naruto if he's in a precarious position on the battlefield.
One type of fanfiction could be where Kyuubi's obsession with Naruto is rooted in seeing Naruto as a symbol of change. Naruto, with his determination, might make Kyuubi, who has been trapped for so long, believe in a different future. In this kind of fanfiction, Kyuubi could constantly be trying to protect Naruto in his own way, even if Naruto doesn't fully understand it at first.
Another aspect in such fanfictions could be the origin of the Kyuubi seal. Some writers might delve into ancient ninja secrets and forgotten jutsu that were used to create the seal in the first place. They might also explore if there were other possible ways to seal the Kyuubi that were considered but not used. This can add a whole new layer of mystery and intrigue to the Naruto universe.
One possible fanfiction could be about Naruto learning to fully control the power of his Kyuubi - enhanced eye. He might discover new abilities like seeing through illusions more easily or being able to project his chakra in a more powerful way through his eyes. This could lead to him having an edge in battles against tough opponents.
The 'naruto is the second kyuubi fanfiction' likely delves into the idea that Naruto has a unique relationship with the Kyuubi that makes him be regarded as the second Kyuubi. This could lead to a whole new set of storylines. It could explore Naruto's training in the context of this new identity. He might need to learn to control new powers or abilities related to being the second Kyuubi. Also, it could show the political and social implications within the ninja world. Villages might be more afraid of him or try to use him for their own purposes. And it could also touch on the origin of this 'second Kyuubi' concept, like if there was some ancient prophecy or some secret experiment that led to Naruto being in this position.
Well, in such a fanfiction, it might explore the power dynamics differently. Danzo, being a powerful figure, if he cares about Naruto, could offer Naruto unique training opportunities. This could lead to Naruto developing new skills and a different relationship with the village. It might also change how Naruto views the more shadowy aspects of the Hidden Leaf, since Danzo is associated with those elements.
Sakura might show her care for Naruto in fanfiction by always being there to heal his wounds. Since she is a skilled medic - ninja, she could be depicted as dropping everything to tend to Naruto whenever he gets injured during a mission or a fight.
Yes, in some fanfictions, Naruto is often depicted as the Kyuubi or having a very close connection to it. This can lead to really interesting and unique storylines that deviate from the original plot.