Well, perhaps a member of the unsub's (the kidnapper's) family or someone close to them has a change of heart. They might contact the BAU secretly and provide information about where Reid is being held. The team could then plan a stealthy operation to get Reid out. Also, Reid is very intelligent. He might be able to manipulate the kidnapper into making a mistake that the BAU can use to their advantage and rescue him.
In the fanfiction world, there could be a lot of creative rescue scenarios. For example, Reid might have befriended someone in the past who has some special skills or connections. This person could show up unexpectedly and help him escape. Or, the kidnapper could have some sort of vendetta against the BAU but Reid manages to convince him that harming him would not achieve his goals. This could lead to the kidnapper releasing Reid on his own accord.
They'll likely interview people who had recent contact with Reid. The team will also analyze any communication from the kidnapper if there is any. Based on their profiling skills, they'll narrow down the suspects and search for the location where Reid is being held. Morgan might use his combat skills and Garcia will be crucial in providing technological support to find Reid.
It could be that Reid has unknowingly crossed paths with a criminal organization. They kidnap him to extract information about the FBI's investigations into their activities. Reid has to endure torture and interrogation, but he also tries to analyze his captors' behavior to find a way to escape.
One possible motive could be revenge. Maybe Reid has put away a relative or someone close to the kidnapper in the past. Another motive might be related to Reid's intelligence. The kidnapper could want to use his brainpower for some illegal or self - serving scheme, like cracking a code or coming up with a complex plan.
One great Reid kidnapped fanfiction is 'The Abduction of Reid' on FanFiction.net. It has an interesting plot where Reid is kidnapped by an unsub with a personal vendetta. The author does a great job of building suspense and keeping the characters in - character.
Another theme is Reid's own personal growth during the ordeal. He may face his fears, or learn something new about himself. For example, in some fanfictions, he discovers a new level of strength or resilience that he didn't know he had while being kidnapped.
One scenario could be that Reid gets hurt during a chase. Maybe he trips and falls while running after an unsub, and sprains his ankle. This would slow him down and make him vulnerable.
One plot could be about how Baby Reid's intelligence makes him an outcast among other babies. He doesn't fit in with the normal baby activities and instead is more interested in observing and analyzing his surroundings. His parents worry about his social development but soon realize that his unique way of seeing the world is a gift. They start to find ways to nurture his intellect while also ensuring he has some form of normal social interaction, which could be a really heartwarming and interesting story.
Often, these fanfics can be a great way to expand on the relationships within the Criminal Minds universe. When Reid is kidnapped, it could bring out different sides of his relationships with his colleagues, like the deep - rooted loyalty and friendship they have for him.
One common theme is Reid's struggle to escape using his intellect. He might analyze his kidnapper's behavior and the environment to find a way out.
In some fanfictions, Reid's kidnapping could be related to his family secrets. Maybe there's someone from his past, like a long - lost relative or someone his mother knew, who abducts him to get to something valuable, either information or an object. This could lead to a lot of self - discovery for Reid as he tries to figure out the motives behind his abduction while also trying to escape.