Maybe it's a new villain in the fanfiction. This villain could be after Luigi because he thinks Luigi has some sort of special power or knowledge. So the villain kidnaps Luigi in a very sneaky way, like using a magic spell to put Luigi to sleep first and then whisking him away to a secret lair hidden deep in a dark forest.
One possible plot could be that Luigi is kidnapped by a group of mischievous goombas who are being controlled by a powerful dark magic user. Luigi, while kidnapped, uses his wits to befriend some of the weaker goombas and gets them to help him send a message to Mario. Mario then has to figure out where Luigi is being held based on the clues in the message.
Yoshi could also be the rescuer. Yoshi has his long tongue that can be used to grab things from a distance. He could use it to pull Luigi out of a locked cage or something. And Yoshi is very fast and can jump high too. So he'd be a great candidate to go on a rescue mission for Luigi.
Well, perhaps it involves Luigi getting some strange illness that no one in the Mushroom Kingdom has seen before. So, Mario and Princess Peach have to search for a cure all over the place. They could meet new characters during their search who either help or hinder them in their quest to make Luigi well again.
Well, in a 'pit gets kidnapped' fanfiction, the plot could involve the search for Pit. Maybe his friends like Palutena start a quest to find him. They might face various obstacles and enemies along the way.
Well, the fanfiction could be that Esme gets kidnapped while she is on her way to an important event. The kidnappers might be holding her for ransom. Her friends then start to look for any clues. They might find out that the kidnappers have a secret hideout in an abandoned building. So they plan a rescue mission, but they have to be careful as the kidnappers are well - armed and dangerous.
It could be that Ginny is kidnapped because she has some special knowledge or power that the kidnappers want to exploit. Her friends form a team to rescue her. Along the way, they discover more about the kidnappers' motives and the true nature of Ginny's importance. There would be elements of mystery, adventure and friendship in the fanfiction.
Well, perhaps Voldemort's followers could kidnap Harry to use him as a bargaining chip. They might hold him in an old, dark wizarding house, guarded by dark magic. Harry would then try to escape using his own magic skills and the help of some unexpected allies like house - elves who secretly oppose Voldemort.
Well, one possible plot could be that the kidnappers are after some valuable information that Castle has. Maybe it's related to a case he was working on and they think he knows more than he actually does. So they take him to a secret location and try to force him to talk.
In a 'damian gets kidnapped fanfiction', perhaps Damian is kidnapped because he has some special knowledge or power. The kidnappers could be a secret organization. His friends might start to search for him, and along the way, they discover secrets about Damian they never knew before. They have to overcome various obstacles to find him, like decoding mysterious messages left by the kidnappers.
Perhaps Hinata is kidnapped because she has some unique power or knowledge that the kidnappers want. In the fanfiction, the story could focus on how she uses her wits and hidden strength to try to escape while her comrades search for her. For example, she might be able to communicate with a small animal in the cell she's held in and use it to send messages.