There could also be a mysterious new supernatural being in the fanfiction. This being, neither vampire nor werewolf, but with its own set of powers, kidnaps Bella because it senses some sort of power within her that it wants to harness for its own purposes.
It could be a rogue vampire. Maybe a vampire who has a grudge against the Cullens and figures that taking Bella is the best way to get back at them. This vampire might be acting alone, thinking that he or she can use Bella to bargain with the Cullens for something they have.
A group of werewolves from a different pack than Jacob's could be the kidnappers. They might believe that Bella is a threat to their way of life because of her relationship with the vampires. So they decide to kidnap her to keep her away from the vampires and protect their territory.
In some of these fanfictions, one plot could be that Bella's kidnapping is part of a scheme by a new vampire coven that wants to use her as bait to lure Edward. They might think that by having Bella, they can draw out Edward and his family and then overpower them to take over their territory.
It could be Discord. He loves causing chaos and kidnapping Twilight Sparkle would be a great way to disrupt the harmony in Equestria. He might do it just for fun or to see how Twilight's friends would react.
Maybe it's a group of poachers who are after rare Pokémon. Gengar, being a relatively unique and powerful ghost - type, would be a valuable catch for them. They could plan to sell Gengar on the black market for a high price.
It could be the Joker. He's always up to no good and kidnapping Robin would be a great way to mess with Batman. The Joker might want to use Robin to force Batman into a series of cruel and twisted games.
Maybe an enemy from another village. If there are political tensions between villages, kidnapping Sarada could be a way to gain an advantage. They might think that by having her, they can force her village to make concessions in treaties or resources.
It could be a new villain who has heard about Tails' mechanical skills. This new baddie might think that by kidnapping Tails, they can force him to build powerful weapons for them.
It could be a rival magic knight. Maybe someone from a different squad who is jealous of Asta's rapid rise in the ranks and the attention he gets. They might think that by kidnapping him, they can make themselves look better or get rid of the competition.
Maybe a human who has discovered the existence of vampires and wants to use Renesmee to prove it to the world. They might think that by kidnapping her, they can expose the vampire world and gain fame or fortune. Another option is a rogue werewolf who doesn't like the alliance between the vampires and werewolves and decides to take Renesmee as a way to break that bond.
One possibility is Dr. Eggman. He has always been after Sonic and wants to stop him. Kidnapping Sonic would be a way for him to achieve his evil goals.
A new villainous trainer group. They might see Ash as a threat to their plans of dominating the Pokémon world, so they kidnap him to stop him from competing in important battles or tournaments.