Another aspect is how it affects the relationships in the story. If Sam is hurt, it can put a strain on his relationship with Dean. Dean might feel guilty for not being able to protect him. Or it could strengthen their bond as Dean devotes all his time to taking care of Sam and making sure he gets better.
One type of fanfiction could be where Sam gets hurt during a hunt. Maybe he's attacked by a powerful supernatural creature and has to deal with a serious injury while Dean tries to find a way to save him. It could explore his physical and mental pain, and how he copes with the situation.
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.
One common theme is Sam's physical pain and how he copes with it. For example, after a fight with a demon or a monster.
One common plotline could be Sam getting physically hurt during a hunt and his brother Dean having to take care of him. For example, in some fanfictions, Sam might be injured by a supernatural creature like a werewolf. Another plotline could involve Sam being hurt emotionally, perhaps due to a betrayal within the hunting community or a difficult decision he has to make. Sometimes, fanfiction writers explore Sam getting hurt as a result of a spell gone wrong, which then leads to a series of events where the other characters have to find a way to reverse the effects.
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.
Well, when Sam dies in a Supernatural fanfiction, it can completely change the direction of the story. It might lead to Dean going on a dark and vengeful path, seeking whoever or whatever was responsible for Sam's death. The remaining characters would have to reevaluate their roles and the purpose of their fight against the supernatural. It could also introduce new characters who are drawn into the chaos that follows Sam's death.
He could be poisoned. There are many supernatural creatures in the Supernatural universe that could use poison. For example, a witch could create a poisoned potion and trick Sam into drinking it.
Some writers will use symbolism to show Sam's pain. For example, if he's been hurt by a dark magic spell, they might describe the darkening of his eyes or a shadow that seems to follow him. And in terms of his emotional pain, they could compare it to a storm brewing inside him, with his thoughts and feelings churning like thunderclouds.
Another option is Tumblr. Some bloggers share links to great 'Supernatural' fanfictions, including Hurt Sam ones. You can search for relevant tags or follow blogs dedicated to 'Supernatural' fanfic recs.
Well, it could be that Sam sees potential for redemption in those who hurt him, or he might feel obligated to try and change them for the better. Another possibility is that he's trapped in a situation where he has no other choice.