The plot could involve Stiles' friends trying to rescue him. They would have to track down Kate and figure out her motives. Along the way, Stiles might try to outwit Kate from the inside. He could pretend to cooperate while secretly planning his escape or trying to send messages to his friends. It could be a story full of mystery, danger, and the bonds of friendship.
In this fanfiction, Kate might be working for a greater evil. She kidnaps Stiles to force him to do her bidding. Maybe she needs him to break into a secure location or decrypt some important information. Since Stiles is often portrayed as clever, she might think he can solve a problem for her.
Stiles' father could be a major character. He would be worried sick about his son and use all his resources to try and find him. Maybe he teams up with some of Stiles' friends like Scott or Lydia.
It could also be for revenge. Perhaps Stiles or someone associated with him has wronged Peter in the past within the context of the fanfiction story. So, Peter kidnaps Stiles to get back at him or those related to him. Another reason might be that Peter is being controlled by some other force. There could be a dark entity manipulating Peter's actions, and it makes him kidnap Stiles for its own sinister purposes.
Well, perhaps Stiles gets used as a bargaining chip against his friends. The alpha pack might want something from Scott or the others, and they think Stiles is an easy target to control them.
Perhaps in this fanfiction, the Alpha pack kidnaps Stiles because they see him as a key to something bigger. Stiles is a very intelligent character, and they might want to use his brainpower for their own evil plans. He could be held in some sort of dark and spooky lair. His friends would then have to figure out where he is, and in the process, they might discover new things about the Alpha pack and their motives. There could also be some internal conflict within the Alpha pack regarding what to do with Stiles.
One common theme is the forced proximity. Since Derek kidnaps Stiles, they are forced to be close to each other. This often leads to a deeper understanding of each other and sometimes the development of romantic feelings.
Survival is also a big theme. Stiles has to figure out how to survive in a dangerous situation with Deucalion. This could involve things like finding food, avoiding other threats in the place where he's held, and dealing with Deucalion's mood swings.
It could also be for power. Perhaps Stiles has some knowledge or ability that Theo wants to use for his own gain. In the show, Stiles was quite smart and resourceful, so Theo might kidnap him to get access to that intelligence or those skills. In some fanfictions, Theo might be trying to use Stiles as a bargaining chip to get something from the other characters like Scott or Derek.
On the other hand, Stiles is also known for his quick thinking. He might start to try and bargain with Peter. He could offer to help Peter in some way if Peter lets him go. For example, if there's a problem in the supernatural community that Peter is facing, Stiles could say he'll use his human ingenuity to solve it. Also, Stiles could be angry. He might start shouting at Peter, calling him out on his actions, and trying to make Peter see how wrong this is.
One common theme is betrayal. Kate often betrays Stiles' trust in these fanfictions, which leads to his emotional and sometimes physical hurt. This theme is central as it drives the conflict in the stories.
One possible plot could be that Stiles is a huge Avengers fan in his own world, and through some magical or scientific mishap, he gets to meet his heroes. But it's not all fun and games. He has to prove himself worthy of being part of their team. He could also bring in some of his own world's technology or ideas that help the Avengers face a new and powerful threat.