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.
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 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 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 great fanfiction idea could be exploring Baby Reid's early signs of his genius. Maybe in the story, even as a baby, he shows an uncanny ability to notice patterns in the simplest of things around him, like the way the leaves fall from the trees in a particular order. It could also focus on how his family first reacted to his extraordinary intelligence, whether they were in awe or a bit scared at first.
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.
Hotch would feel a great sense of responsibility. He's the leader, and Reid getting hurt might make him question his decisions that led to the situation. He'd be very protective and focused on getting Reid back to full health.
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'.
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.
One possible direction for the fanfic could be a sort of 'what - if' scenario. For example, what if Reid's injury had long - term consequences? It could change his role in the BAU, his relationships, and even his approach to solving cases.