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.
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.
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.
He could use his intelligence to manipulate Kate. Maybe he convinces her that he is more useful to her if he is free, and she lets her guard down long enough for him to make a run for it. Also, he could have some hidden skills or knowledge that he uses to break free. Say he knows a spell or a code that unlocks his restraints or the door to his prison.
Scott would be the most likely one. He's Stiles' best friend and the True Alpha. He would never let the Alpha pack harm Stiles and would go to great lengths to rescue him.
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.
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.
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.