Another trope is the 'mysterious injury'. Dean gets hurt by some unknown or supernatural force. This then leads to an investigation to find out what caused the injury and how to stop it from happening again. Writers use this to create suspense and mystery in the story, keeping readers on their toes as they follow Dean's journey to figure things out while dealing with his pain.
You can try Archive of Our Own (AO3). It has a vast collection of Supernatural fanfictions, including ones where Dean gets hurt. Just use the search function and type in relevant keywords like 'Supernatural Dean hurt'.
The 'alternate universe' trope is quite common too. For example, there are fics where Dean and Castiel are in a modern - day high school setting instead of the supernatural world they're usually in. It gives a fresh take on their characters and relationship.
There's a fanfic called 'Dean's Pain'. In this, Dean gets seriously hurt by a supernatural creature. It delves into how he copes with the pain both physically and mentally, and also how his friends in the hunting community rally around him. It's a really engaging read as it not only focuses on his injury but also on the relationships in his life.
One example could be a fanfiction where Dean is physically hurt during a hunt gone wrong. Maybe he's attacked by a powerful demon and sustains serious injuries. This can add drama and tension to the story as other characters, like Sam, have to find a way to save him.
Physically, he could be shown with bruises, cuts, and broken bones. Writers might describe his pain in detail, like how he winces when he moves or how difficult it is for him to stand. This makes the reader empathize with his situation.
The theme of Dean being tortured by supernatural forces is also quite common. This could be at the hands of demons or other malevolent entities. It not only shows his physical pain but also his mental strength in trying to endure such torture. Additionally, there are fanfictions where Dean's hurt is related to his inner struggle with his identity as a hunter, a brother, and a man, which adds an extra layer of complexity to the story.
Perhaps Sam gets hurt while trying to protect a civilian. He jumps in front of a werewolf's attack meant for someone else. This would show his selfless nature. The local hunters in the area might not trust Sam and Dean at first, but seeing Sam's sacrifice could change their minds, adding an interesting dynamic to the story.
Sometimes it's due to Dean's overprotectiveness. He might think he's doing what's best for Sam but in the process, his actions end up causing harm. For instance, he could keep Sam from a mission that Sam believes is important, and in the struggle, Sam gets hurt.
One popular story could be about their adventures together against a powerful new enemy. In the fanfiction, they might have to rely on each other's unique skills. Gabriel with his trickster abilities and Dean with his hunting expertise.
One popular trope is the 'hurt/comfort' scenario. For example, Dean gets injured on a hunt, and Cas takes care of him, which leads to a tender moment and a kiss. It plays on the emotional bond between them and the protectiveness they feel for each other.