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 scenario could be Reid getting kidnapped by an unsub. The unsub might torture him physically and psychologically, like depriving him of sleep and constantly taunting him about his past traumas. This would be really painful for Reid and make for a very angsty fanfic.
In many Reid - gets - shot fanfictions, it often focuses on the team's reaction. His friends, like Morgan and Garcia, would be extremely worried. They might rush him to the hospital while trying to keep their emotions in check. The angst and worry would be palpable as they wait for news on his condition.
You can try fanfiction websites like Archive of Our Own (AO3). There are likely many stories there about Reid getting hurt in Criminal Minds. Just use the search function and type in relevant keywords like 'Criminal Minds Reid hurt'.
Some fanfictions might also focus on the mystery or the circumstances surrounding Reid's injury. It could be related to a case they were working on, and the story delves into how the team tries to solve the mystery of who hurt Reid and why, all while dealing with the fact that he's injured.
One common theme is Reid's vulnerability. Fans often explore how his intelligence and unique personality can make him a target in different ways. For instance, in some fics, his prodigious memory might be used against him, leading to his emotional or physical hurt.
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.
One popular fanfiction might be 'The Darkest Hour for Reid'. In it, Reid endures both physical and psychological torture, which really tests his character. It shows his resilience and the team's desperate attempts to rescue him.
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 great place to find Criminal Minds Hurt Reid fanfiction is Archive of Our Own (AO3). There are numerous stories there. For example, 'Fractured' which delves deep into Reid's emotional turmoil after a particularly harrowing case. It really captures his vulnerability and the team's reaction to his pain.
One common plotline is Reid getting physically injured during a case. For example, he might be shot while trying to apprehend a suspect. This then leads to the other team members worrying about him and his recovery process.