In most of these fanfictions, Stiles first reacts with shock. I mean, being kidnapped out of the blue is no small thing. But then he quickly tries to analyze the situation. He might start looking for weaknesses in Peter's setup or try to figure out Peter's motives. He often uses his sharp mind to try and find a way to escape or at least gain some sort of advantage over Peter. In some cases, he also tries to appeal to Peter's better nature, if there is one, by talking about things like morality and the consequences of his actions.
Stiles usually reacts with a mix of fear and defiance. He's afraid because he's in a dangerous situation, but his strong - willed nature makes him defiant. For example, in many fanfictions, he'll shout at Peter, trying to show that he won't be easily broken.
Stiles' reaction is complex. At the start, he's likely to be terrified, especially if he's alone and at Peter's mercy. However, as time passes, his survival instincts kick in. He could start to play mind games with Peter. He might pretend to be more compliant than he really is to lull Peter into a false sense of security. And he'll always be thinking about his friends and how they might come to his rescue. He'll try to leave clues if possible, or at least not do anything that would make it harder for his friends to find him.
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 extremely worried and immediately start planning a rescue mission. He'd be angry at Theo for targeting Stiles and would use his alpha powers to try and track him down. He might also call on the rest of the pack for help, like Lydia, who could use her banshee powers to sense if Stiles was in danger or where he might be.
Stiles might initially be shocked. He has been a part of the pack for a long time, and Scott kicking him out would be completely unexpected. He could stand there in disbelief, unable to process what has just happened.
At first, it might be a tentative alliance. Stiles could be initially drawn to Peter for his knowledge. Peter, seeing Stiles' potential, starts to include him more in his plans. As time goes on, they might develop a mutual understanding. Stiles begins to trust Peter more and more, and Peter starts to value Stiles not just for his help but also as a friend or something more.
There's a fanfic called 'Peter's Kidnapped Prize'. It starts with a very intense kidnapping scene. As the story progresses, it shows how Stiles' friends are trying to find him, and at the same time, Stiles is trying to survive in Peter's clutches. 'Stolen by Peter' is another one. It's unique in the sense that it shows a different side of Peter, not just as a villain but as a complex character with his own reasons for kidnapping Stiles. 'The Kidnapping of Stiles' also stands out as it weaves in some elements of mystery about why Peter chose Stiles in particular.
Some members of the pack might be angry at first. They could see his leaving as a betrayal, especially if they are in the middle of a difficult situation and rely on him in some way.
It could be that Stiles is in some kind of danger, perhaps from another supernatural being. And he goes to Peter because Peter has certain powers or knowledge that could protect him. For example, Peter might know how to defeat a particular enemy or how to get out of a tricky situation involving magic or some other supernatural element.
Some of his friends might be really surprised. Scott, for example, might be a bit worried that Stiles' vampire obsession could lead him into dangerous situations. Lydia, on the other hand, could be more intrigued and might want to know more about the fanfiction. She might see it as an interesting intellectual pursuit.
There could be other members of Peter's pack such as Derek. Derek often plays an important role in stories related to packs. He might be initially skeptical of Stiles being part of the pack.