In such a fanfiction, Naruto's friends would likely go on a desperate search for him. Sasuke might put aside his pride and team up with the others. They would follow any leads, like tracking the kidnapper's chakra signature if possible.
If Naruto is kidnapped by Kumo in fanfiction, it could lead to a series of intense battles. Naruto himself might try to escape on his own using his ninja skills and the power of the Nine - Tails. His captors in Kumo would probably want to extract some sort of information from him, like the secrets of the Nine - Tails or Konoha's defense strategies. However, Naruto is a tough character and would surely put up a fight.
In fanfiction, if Naruto gets kidnapped by Akatsuki, he might be used as a bargaining chip. The Akatsuki could try to exchange him for something valuable like the Nine - Tailed Fox's chakra. Or they might try to extract the Nine - Tails from him forcefully. Naruto would surely put up a fight though, using his Rasengan and other jutsu.
Well, in most cases, his friends would likely try to rescue him. Sasuke might put aside his differences for a while and join forces with Sakura and the others. They'd probably start by gathering information about the council's motives and the location where Naruto is being held.
If Naruto and Hinata were kidnapped by Kumo in fanfiction, it could lead to a major diplomatic crisis between the Hidden Leaf and Kumo. Naruto, being the hero of the Hidden Leaf, his kidnapping would enrage the villagers. Hinata, as his wife, her kidnapping would add to the urgency. Kumo might have kidnapped them for Naruto's power or to use Hinata as a hostage to gain some sort of leverage over the Hidden Leaf. The Hidden Leaf would then have to figure out a way to rescue them without starting a full - scale war.
In such a fanfiction, Naruto might be used as a pawn by Kaguya. Maybe she wants to extract the Nine - Tails' power from him. She could also try to manipulate Naruto's strong will to serve her own purposes, like using his influence among the shinobi world to regain control.
Well, Naruto could potentially be used as a bargaining chip by Orochimaru. Orochimaru might try to trade Naruto for something he wants from Konoha, like secret jutsu scrolls or some kind of political power within the village. And Naruto, being the determined hero he is, would likely be constantly looking for a way to escape and foil Orochimaru's plans.
Well, in this kind of fanfiction, usually the main character might be in a state of fear at first. They could be held in a spooky castle or lair of the vampire prince. Maybe they would try to escape but find it difficult due to the vampire's powers and the unfamiliar surroundings.
In fanfiction, if Deku gets kidnapped, his friends from U.A. High would likely launch a rescue mission. Bakugo might be especially determined, as much as he tries to hide his concern. They would use their quirks in creative ways to track Deku down.
In the 'sonic is kidnapped by scourge fanfiction', Sonic's friends would surely be worried sick. Tails might start using his gadgets to track Sonic down. Meanwhile, Sonic himself would be constantly thinking of a way out. Scourge could have kidnapped him for various reasons, like to prove he's stronger or to get some sort of information from Sonic. Sonic would not go down without a fight though, and he'd be looking for any opportunity to break free and foil Scourge's plans.
In a Destiel - centered fanfiction where Sam is kidnapped, perhaps it's all part of some grand scheme to make Dean realize his true feelings for Cas. The kidnappers might be some over - zealous fans within the story who think that by causing chaos, they can bring about the Destiel endgame. They could hold Sam in some strange, other - dimensional location and send Dean and Cas on a quest to find him.