If Sam is kidnapped in Supernatural fanfiction, it could be a personal vendetta. There might be a hunter who has a grudge against the Winchesters and decides to target Sam. This hunter could have a different view on how to deal with the supernatural and thinks the Winchesters are too lenient. So, they kidnap Sam to make a point or to try and force Dean to change his ways. It would create a lot of tension and conflict within the Supernatural community in the fanfiction.
In fanfiction, if Sam was kidnapped, it could lead to a very intense story. Dean would surely go on a rampage to find him. Maybe Sam was kidnapped by a powerful demon who wants to use him for some dark ritual. It could also be a new, unknown enemy who has a vendetta against the Winchesters.
One idea could be that Sam is kidnapped by a group of rogue hunters who think he's gone too far in his use of demon powers. They lock him in an abandoned bunker and try to 'exorcise' the 'demon' out of him, not realizing he's in control. His brother Dean has to race against time to find him, following a series of cryptic clues left by the kidnappers.
Well, Dean would probably go into full - on search - and - rescue mode. He'd start by reaching out to all their contacts in the hunter community. Maybe he'd call Bobby in spirit form if he could, asking for any leads or advice. He'd also check Sam's last known locations and look for any signs of a struggle.
One possible scenario could be that Sam betrays Danny's secret identity to someone he doesn't trust, like a ghost hunter. Maybe she does it out of jealousy if Danny starts getting closer to another character.
One possible scenario could be that Nightwing is kidnapped by a new supervillain who wants to use him as bait to lure Batman. The villain might hold Nightwing in an abandoned warehouse, setting up various traps. Another could be that a criminal organization kidnaps him to extract information about the other heroes in Gotham. They might use high - tech devices to try and break his will.
Well, perhaps a member of the unsub's (the kidnapper's) family or someone close to them has a change of heart. They might contact the BAU secretly and provide information about where Reid is being held. The team could then plan a stealthy operation to get Reid out. Also, Reid is very intelligent. He might be able to manipulate the kidnapper into making a mistake that the BAU can use to their advantage and rescue him.
Well, it could be that Clarke is kidnapped by a group who wants to use her knowledge for some devious plan. Bellamy, being her closest ally, uses his tracking skills to find her. He might also discover some secrets about Clarke's past during the rescue journey. And along the way, their relationship could deepen even more.
In some fanfictions, it could be a miscommunication situation. Sam might think he's doing the right thing in a hunt, but John disagrees. So, John spanks Sam not just as a punishment but also as a way to make him see his perspective. Also, it could be related to Sam's relationship with the supernatural side of himself. John might be trying to keep Sam's human side dominant by using this rather extreme form of discipline.
One common theme is the struggle for survival. Sam has to find ways to endure the situation he's in while kidnapped. For example, in many stories, he might have to deal with lack of food or water.
Perhaps Gray and Erza lead a search party. Gray could use his ice - make magic to freeze any obstacles in their way while Erza, with her many armors and combat skills, could fight off the kidnappers. They might also get some help from the other guild members like Wendy, who could heal Natsu if he's been injured during the kidnapping and torture.