A sense of duty is present as well. Dean feels it's his duty to keep Sam safe. So when Sam is hurt, it's like he's failed in his mission. This leads to self - reflection in Dean and often a new determination to keep Sam out of harm's way in the future.
In Hurt Dean Winchester fanfiction, a frequent theme is his self - sacrifice. Dean is always putting himself on the line for others in the show, and in fanfictions, this is often exaggerated. He might sacrifice himself in a big way and then have to face the consequences while being hurt. Also, the theme of his past traumas resurfacing when he gets hurt is quite common. His experiences in Hell, for example, might come back to haunt him when he's physically or emotionally injured.
The theme of family legacy is quite prevalent. Since they come from a family of hunters, many fanfictions explore how this family history affects their actions and decisions. Also, the theme of growing up in a tough environment is common. They face a lot of hardships at a young age, and fanfictions often depict how they cope with it and become stronger.
Since I don't actively engage with this type of fanfiction, I can't say for sure. But generally in fanfiction, themes might include the intense emotional connection between the characters, perhaps with a romantic or sexual undertone.
One common theme is the exploration of their deep emotional bond in a romantic context. Since they already have a strong brotherly bond in the original show, fanfictions often build on that to create a more intimate, romantic relationship.
One common theme is the bond between the brothers. When Dean is hurt, it tests and strengthens their relationship. Another theme could be sacrifice. Sam might be willing to sacrifice his own well - being or safety to protect the injured Dean. Also, there's often the theme of recovery, not just physical but also emotional as Dean recovers from his injury with Sam's support.
One great Sam Hurt Dean Winchester fanfiction is 'The Broken Bond' which delves deep into the emotional turmoil when Sam is hurt and how it impacts Dean. It shows Dean's struggle to protect his brother and his own internal conflicts.
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.
A recurring theme is the search for their place in the world. As hunters, they don't really fit into normal society. Fanfictions explore how they deal with this outsider status. Another theme is the power of friendship. They have friends in the hunting community, and how those relationships interact with their brotherly bond is often a topic. Also, the theme of fate and free will comes up, as they seem to be following a certain path but also trying to break free from it sometimes.
One common theme is the struggle between good and evil. Dean often has to decide whether a vampire can be redeemed or is just pure evil. Another theme is the idea of family. His relationship with Sam and how vampires can either threaten or be integrated into their 'family' unit in a strange way. Also, there's the theme of sacrifice. Dean might have to sacrifice his own safety or even his beliefs to deal with the vampire situation.
One common theme is the idea of the oc being a powerful ally or a love interest for Dean. For example, many fanfictions have an oc with special powers that help Dean in his hunts.