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 could be recovery. After being hurt, the story might focus on how Chase Davenport overcomes his injuries or emotional trauma.
Love and relationships also show up. It could be his relationship with his enemies or the idea of him falling in love, which is an interesting contrast to his usually cold and powerful persona.
One common theme is the power struggle. The chasers, usually hunters, are often seen as the representatives of order and humanity, while the vampires represent chaos and the unknown. Another theme is the pursuit of immortality. Sometimes the hunters are after the vampires not just to kill them but also to discover their secrets of eternal life.
Another theme is heroism. They are often depicted as heroes in fanfiction, saving the day in different situations. This could be rescuing someone from a burning building or finding a lost item. It shows their brave and helpful nature. Also, teamwork is a big part of it. They work together, using their unique skills to achieve a common goal, like Chase's police skills and Marshall's firefighting abilities combining to solve a problem.
Adventure is also a big theme. Since they are part of a rescue team, many fanfictions involve them going on exciting adventures together, like exploring uncharted territories or facing dangerous villains.
One common theme is his growth as a doctor. Writers often explore how he hones his skills and gains more confidence in his medical abilities.
Friendship is a common theme. Their bond as brothers and friends is often explored, like how they support each other through tough times.
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.