Often, the theme of redemption plays a part. Maybe Rossi has made some mistakes in the past and getting hurt is a sort of atonement or a chance for him to start anew. Also, the exploration of his past traumas is a common theme. His hurt can trigger memories of old wounds, both physical and emotional, and the fanfiction might delve into how he copes with those resurfacing issues.
One common theme is his vulnerability. When Rossi is hurt, it shows a side of him that is not always visible in the show. Another theme could be the support he gets from his colleagues. They come together to help him through the tough time, highlighting the strong bond between them.
One common theme is mentorship. Often, Rossi takes on the role of a mentor to the OC, guiding them in the ways of the BAU. For example, in many stories, he teaches the OC about profiling techniques.
One common theme is mentorship. Rossi being an experienced agent, often takes the reader under his wing to teach them about the world of criminal investigation. For example, in many stories, he imparts his knowledge of profiling.
Family relationships are a very common theme. Since it's about Rossi's sister, exploring how they interact as family members, with all the love, conflicts, and support that comes with it. Another common theme is mystery. Given the Criminal Minds setting, the sister might be involved in some sort of mystery related to the BAU's cases.
Well, you can try looking on popular fanfiction websites like Archive of Our Own. Just search for 'Hurt Rossi' there, and you'll likely find a variety of stories. Some might focus on his emotional hurt, perhaps dealing with a difficult case that takes a toll on him, while others could be about physical harm and his journey to recovery.
One common theme could be the relationship development. Since they are from different generations, there might be a theme of bridging the gap, both in terms of age and different outlooks on life.
One common theme could be emotional pain. Maybe Arthur has been betrayed by someone close to him, and the fanfiction explores his journey of dealing with that hurt. For example, if a friend he trusted turned out to be a traitor.
One common theme is isolation. Magnus might be isolated due to his unique powers or past traumas, which causes him pain. For example, in some fics, his immortality makes him feel alone.
One common theme is Haru's emotional isolation. Often, fanfictions in this genre show Haru feeling alone despite being surrounded by people.
Another theme is revenge. Sometimes the reason for the chase is revenge, and the hurt that comes to the chased character is a part of that revenge plot. It can make for a very dramatic story as the character tries to either escape or turn the tables.
One common theme is isolation. When Juvia is hurt, she often isolates herself, feeling that she has to deal with her pain alone. For example, in many stories, she might retreat to a secluded place after a particularly bad emotional or physical injury.