One key element is the exploration of their loyalty to Voldemort. Their actions as Death Eaters are often central. For example, in many fanfics, they are shown carrying out his orders together.
Maybe the fanfic often misrepresents the nature or relationship of Bellatrix and Rodolphus. For example, if in the original they are portrayed as very dark and loyal to a certain cause, but fanfic makes them out to be something else entirely, like soft or good - hearted, it could lead to dislike. Also, some people who are die - hard fans of the official story just don't like the idea of others taking creative liberties with their beloved characters.
In a particular fanfic, their daughter could be sent on a secret mission by Voldemort. However, during the mission, she discovers the true horrors of the Death Eaters' actions. This realization makes her question her loyalty to Voldemort and her family. As a result, she has to find a way to either hide her new - found beliefs or risk everything to oppose them.
One common theme is their loyalty to Lord Voldemort. Fanfics often explore how their allegiance to the Dark Lord affects their relationship with each other. For example, they might have to make sacrifices in their marriage for the sake of serving Voldemort.
Perhaps there could be some sort of 'quality control' in the fanfic community for stories related to Bellatrix and Rodolphus. This could be in the form of peer - review or a set of guidelines for writing about these characters. By having a standard, the overall quality of the fanfic could improve, and potentially reduce the hate from fans of the original characters.
One popular Bellatrix Rodolphus fanfic is 'The Darkest Bond'. It delves deep into their relationship within the dark wizarding world. It shows how their loyalty to Voldemort also affects their connection with each other.
I'm not sure if there is such a specific fanfiction. It's a rather unusual and dark concept considering Bellatrix's loyalty to Voldemort and her actions in the original story. Fanfiction can be very diverse, but this would likely be a very niche and perhaps controversial take on the Harry Potter universe.
Fanfiction.net might also be a place to look. Some authors on that platform create really interesting stories about these two characters. Just search for 'Bellatrix and Rodolphus Lestrange' in the search bar, and you'll get a list of relevant fanfics. However, the quality may vary, so you might need to read a few to find the really good ones.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a vast range of wild and creative ideas, but this one seems rather unusual. It goes against the original lore in many ways. In the original 'Harry Potter' series, Harry is James and Lily's son, and Bellatrix is a Death Eater who has a completely different story arc.
One common theme is loyalty. Since they are both Death Eaters, their loyalty to Voldemort and to each other is often explored. For example, in many fanfictions, they will go to great lengths to protect each other in the name of their shared cause.