Perhaps the kidnappers have a specific motive related to Duke's unique abilities. They could be trying to force Duke to use his powers for their own evil purposes. Duke, being a strong - willed character, would resist and try to find a way to escape from captivity on his own while waiting for rescue.
One possible plot development could be that Duke's friends in the Bat - family immediately start a search operation. They might use their various skills and resources to track down the kidnappers. For example, Batman could analyze the crime scene for any clues while Robin tries to hack into security cameras in the area.
Another development could be that Duke discovers he has some new, unexpected powers while in captivity. This new discovery gives him an edge in his attempts to break free from the kidnappers. He might also form an unlikely alliance with one of the kidnappers who has a change of heart.
Well, one possible plot development could be that the kidnappers demand a ransom from Batman. Batman then has to race against time to find Robin without alerting the media or causing panic in Gotham. Another development might be that Robin manages to leave some hidden clues for Batman to find while being held captive. Maybe he uses his martial arts skills to briefly overpower one of the kidnappers and mark a symbol on the wall that only Batman would understand.
One possible plot development could be that his friends immediately launch a rescue mission. They might use their unique skills and resources to track down the kidnappers. For example, if Obi - Wan is involved, he could use his Jedi mind tricks to interrogate possible informants in the underworld.
A new, unknown criminal organization could be behind the kidnapping. They might have heard about Duke's potential and see him as a valuable asset. They could be planning to either brainwash Duke to join them or use his abilities to carry out their illegal activities.
One possible plot development could be that the guild members quickly realize Lucy is missing and start a search. Natsu, being her closest friend, might lead the charge. They could follow any clues left behind, like a piece of Lucy's clothing or a strange magical residue. Another development could be that the kidnappers demand a ransom from the guild in the form of a powerful magical item. The guild then has to decide whether to give in or find another way to rescue Lucy. Or perhaps Lucy manages to escape on her own using her Celestial Spirit powers. She could call upon one of her spirits, like Leo, to help her break free from her bonds and then find her way back to the guild while avoiding the kidnappers.
In this fanfiction, perhaps Harry is kidnapped by the Order because they think he's being influenced by dark forces. As the story unfolds, he could start to understand their reasons while also uncovering a traitor within the Order who wants to harm him for real. Or, he might use his skills to turn the situation around and make the Order see that they were wrong to kidnap him in the first place. He could then lead them in a new direction against Voldemort.
One possibility is that Naruto's friends launch a rescue mission. They would use their unique skills, like Sasuke's Sharingan or Sakura's medical ninjutsu combined with her combat skills, to find and save Naruto.
Perhaps Sakura's injury makes her realize she has some hidden strength within her. She could start to have visions or gain new abilities while she's recovering from the stabbing. This could then lead to a whole new arc in the fanfiction where she has to learn to control these new powers.
Well, one possibility is that Merlin's friends, like Arthur, might search desperately for a cure. They could go on a dangerous quest to find a rare herb or consult a powerful sorcerer who might know how to save him. Another could be that Merlin, while poisoned, has strange visions or dreams that give him clues about his true destiny or the future of Camelot.
Well, one possible plot development could be that after Christy gets shot, her friends or family rush to her side and try to find the person who did it. Maybe they start to investigate and discover some secrets in the process.
One possible plot development could be that Beckett's friends and colleagues are in a race against time to find the shooter. They might follow various leads, interrogate suspects, and gradually piece together the mystery behind the shooting.