It's possible that the collective of the characters in the yaoi fanfiction decides to punish Kakashi. They all feel that his actions have had a negative impact on their world, so they come together and decide on a form of punishment for him.
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.
Maybe it's an elder or a leader in the fictional world of the fanfiction. They are in charge of maintaining order and when Kakashi steps out of line, they are the ones to dish out the punishment.
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.
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.
Some rogue ninja from other villages might be the ones. They could see Kakashi as a symbol of the Hidden Leaf's strength and think that by torturing him, they can demoralize the village. Also, a new and unknown enemy created specifically for the fanfiction could be the torturer, with their own motives like wanting to steal Kakashi's knowledge of ninja techniques.
In some fanfictions, when Kakashi finds Naruto, it could be a situation where Naruto is in danger. Kakashi would then rescue him and from that moment on, their bond becomes even stronger. Kakashi might then focus on helping Naruto control the Nine - Tails' chakra more effectively, which would change the course of Naruto's development in the story.
Often, Gai is paired with Kakashi in Hurt Kakashi fanfiction. Gai, with his unwavering belief in friendship and his eternal rivalry with Kakashi, can be a great character to interact with a hurt Kakashi. He might try to pull Kakashi out of his slump through their friendly competition. Also, Rin is sometimes included. Since she has a significant past with Kakashi, her presence in the fanfiction can either be a source of comfort or more pain, depending on how the story is written.
Yaoi punishment manga often involves intense and sometimes controversial themes related to punishment or disciplinary actions within a yaoi context.
One possible motive could be to help Naruto control the Nine - Tails' chakra better. Hypnosis might be a way to reach into Naruto's subconscious and find a way to coexist with the powerful force inside him.
Kakashi could use his Sharingan to analyze Obito's moves and find a weakness in his defenses. Since he has the Sharingan, he might be able to predict Obito's attacks and counter them effectively, eventually finding an opportunity to break free.
Often, Naruto is paired with Kakashi in such fanfictions. Their bond from the original series can be explored in new ways in the context of Kakashi's reincarnation. For example, Naruto might be the one to discover Kakashi's reincarnated form and help him adjust.