Maybe it's a revenge plot. Sakura was involved in treating a patient who was related to the kidnappers, but unfortunately the patient didn't survive. The kidnappers blame Sakura and take her from the hospital to make her pay. They could take her to an abandoned building and hold her hostage there.
One idea could be that the kidnappers are after Sakura because she has some special medical knowledge or a unique ability that was discovered during her hospital stay. For example, she might be able to communicate with a certain type of supernatural being, and a secret organization wants to use her for their own gain.
Another plot could involve a case of mistaken identity. There is another person in the hospital who is the real target of the kidnappers, but they mistake Sakura for that person. As they take her away, Sakura tries to convince them of their mistake while also trying to find a way to escape.
Sakura being kidnapped could lead to a lot of character development in the fanfiction. Maybe she tries to escape on her own while Naruto and the others are on their way. She could use her medical ninjutsu skills to heal herself if she gets injured during the escape attempts. Meanwhile, Team 7 might also have to face some internal conflicts during the rescue operation, like differences in their strategies, but in the end, they will surely come together to save Sakura.
One idea could be that Natsu is kidnapped by a dark guild who wants to use his dragon slayer magic for their own evil purposes. They might try to force him to reveal the secrets of his magic or use him as a weapon against Fairy Tail.
It could be a rival ninja clan if this is in a ninja - themed story. They might see Sakura as a valuable asset to get information about her own clan or to use her skills against her people.
One idea could be that Alexis is a princess in the castle. A rival kingdom's forces kidnap her to use as a bargaining chip in a territorial dispute. Her loyal servants then set out on a secret mission to rescue her, facing various challenges along the way.
One possible plot twist could be that Itachi has been mind - controlled to kidnap Sakura. Maybe an enemy of Konoha has a powerful jutsu that forces Itachi to do this against his will. Another twist could be that Itachi kidnaps Sakura as a means to protect her from a greater threat in the shinobi world that no one else is aware of yet. He might know that she has some sort of power or knowledge that makes her a target, and by kidnapping her, he can keep her safe in a hidden location.
Well, perhaps in the fanfiction, Sakura is kidnapped by Sasuke because he wants to use her as a bargaining chip against Konoha. Then, the story could involve the other Konoha ninjas coming together to strategize a rescue mission. They might have to deal with Sasuke's new and powerful abilities that he has acquired during his time away. Sakura, while kidnapped, could also try to talk some sense into Sasuke, appealing to their past friendship and her feelings for him.
A really unexpected plot twist could be that the kidnappers are actually the good guys in a convoluted way. Maybe they know of a prophecy that Sasuke and Sakura are fated to bring destruction, so they are trying to stop it. Another idea is that during the kidnapping, Sasuke and Sakura end up in a different dimension where they have to rely on each other in completely new ways. Plus, the motives of the kidnappers could be related to a secret that Sakura has been hiding about her family all along.
A possible plot is that Shikamaru is kidnapped by a rival village that believes his strategic mind can give them an edge in an upcoming war. His kidnappers try to brainwash him into working for them. However, Shikamaru uses his wits to resist and also leaves subtle clues for his comrades to find him. His friends, on the other hand, must infiltrate the rival village without getting caught to rescue him.
One idea could be that MacGyver is kidnapped by a group who wants him to build a dangerous weapon for them. He has to use his wits and the limited resources in his captivity to not only escape but also prevent the weapon from being built. Another plot could involve MacGyver being kidnapped by a rival agency who wants to steal his secrets and tradecraft. He then has to outsmart them by creating diversions and makeshift tools within the confined space. A third idea is that he is kidnapped by someone seeking revenge for a past mission gone wrong, and he has to convince his captor of his innocence while finding a way to break free.
One idea could be that Legolas is kidnapped by an old enemy of the elves. This enemy might want to use Legolas as a bargaining chip to get some powerful elven artifact. Another plot could involve a powerful dark magic user who kidnaps Legolas to drain his life force which is believed to be very strong due to his elven heritage. A third option is that he is kidnapped by a group who mistakes him for someone else who has great value to them.