Maybe an old enemy who was thought to be defeated but has somehow returned stronger. Orochimaru could be a possibility. He was always obsessed with power and immortality. If Naruto is revived, Orochimaru might see it as an opportunity to study Naruto's new state of being (since he was revived) and use that knowledge for his own dark purposes.
I'm not aware of any such fanfic. Naruto is a male character in the series, and such a concept goes against the natural order of the Naruto universe. Fanfics usually follow the general theme and characteristics of the original work, and this seems quite out of place.
It could be the dominant character in the yaoi pairing. If there is a strong - willed character in the relationship, they might take it upon themselves to punish Kakashi for interfering or causing trouble.
Perhaps it's an organization that wants to use Kakashi for their own evil plans. They might think that Kakashi's skills and knowledge would be useful for them. For example, they could be trying to create some sort of super - weapon and they need Kakashi's expertise in ninjutsu.
Well, his friends might launch a rescue mission. They would use their various skills to track down where Kakashi is being held. Naruto could use his shadow clones to search different areas, while Sasuke might use his Sharingan to detect any hidden threats on the way to the rescue.
One way could be through words of wisdom. Kakashi has a lot of life experience and could share his insights with Sasuke, like how to deal with his inner turmoil and the path he should choose. For example, he might tell Sasuke that revenge isn't always the answer and that there are other ways to find peace.
An unexpected ally could be an old enemy from his past. Maybe a Hollow that he once fought and defeated now sees a greater threat in the situation after Ichigo's revival and decides to team up with him. For example, the Hollow might have information about the new forces that are emerging since Ichigo's return and offers to share that in exchange for some form of protection or mutual benefit.
In some fanfictions, it could be due to a special jutsu gone wrong. Maybe a jutsu that Kakashi was using to transfer some of his chakra to Naruto for a mission accidentally transferred his Sharingan power as well.
One possible plot could be that in the yaoi fanfiction world, there are certain unspoken codes or etiquettes. Kakashi, being unaware or simply ignoring them, does something that is considered inappropriate. As a result, his punishment could range from public shaming within the fictional community to being forced to make amends in a rather difficult or embarrassing way. For instance, he might have to publicly apologize to the characters he has wronged while wearing some sort of humiliating outfit.
If Naruto was raised by Kakashi in fanfiction, their relationship would be very different from the original. Kakashi could teach Naruto more about the Sharingan and its secrets since he has one. Naruto might also inherit some of Kakashi's reading habits and love for Icha - Icha Paradise, which could lead to some really funny moments.