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'.
Often, other characters might come to Dean's aid. Castiel could use his angelic powers to heal any internal injuries Dean might have sustained. There are fanfictions where Castiel hovers over Dean, his blue - eyed stare intense as he channels his grace to heal Dean's head injury from being knocked out.
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.
The other hunters in the Supernatural world, like Bobby if he was still alive in the fanfic, would also be worried. They'd offer their expertise and resources to help Dean. Bobby might give Sam some advice on how to take care of Dean while he's unconscious and how to find the culprit.
Appropriateness is subjective to some extent. While some people might be interested in exploring the darker sides of a character like in 't challa gets tortured fanfiction', others may find it offensive or disturbing. If the fanfiction contains excessive violence and torture without any redeeming narrative or moral exploration, it's likely not appropriate.
I'm not sure specifically as there could be many different interpretations of such a fanfiction. It might involve a character named Neal facing some form of extreme distress or harm within the context of a fictional story created by fans.
It's not extremely common, but it does exist. Some fans are interested in exploring how Naruto would react under extreme duress. However, many other types of fanfiction, like Naruto's training arcs or his romantic relationships, are more prevalent. But still, for those who like a more edgy and intense story, 'naruto gets tortured fanfiction' can be appealing.
Dean would probably be extremely confused at first. He might stand there, staring at his car with a bewildered look on his face, muttering things like 'This can't be real'.
No. Fanfiction is meant to be a celebration of the source material and its characters. Torturing a character in a fanfiction is not in line with this purpose. It can create a negative and uncomfortable reading experience. There are so many other positive and interesting aspects of the characters and the story world that can be explored in fanfiction rather than focusing on torture.
In fanfiction, Dean as a Prince of Hell can open up many interesting storylines. One possibility is that his character becomes darker and more conflicted. He might struggle with his newfound powers and the evil that comes with being a Prince of Hell. His relationships with Sam and Castiel would also be severely tested as they try to figure out how to deal with this new Dean.