Definitely. In the original plot, Bellatrix is a loyal follower of Voldemort and would never be expected to save Harry. But in a fanfic, the author can rewrite the rules. It might be that the fanfic delves deeper into Bellatrix's character, showing that she is not just a one - dimensional villain. There could be a moment of redemption for her, where she realizes that Harry represents something more important than her loyalty to Voldemort, and this realization drives her to save him.
She might be motivated by a long - lost connection. For instance, if there was a family tie between Harry and her that she was previously unaware of. Or perhaps she has a change of heart after seeing the true nature of Voldemort's actions and decides that Harry is the only hope to stop the chaos and destruction Voldemort is causing. It could also be that she is magically bound to save Harry due to some ancient spell or prophecy that she discovers.
The plot could involve the son trying to redeem his mother's name. He might go on a journey to find out more about her past, hoping to understand why she became so evil. Along the way, he meets various characters who knew his mother and has to deal with their mixed reactions towards him.
Voldemort is often paired with Bellatrix in fanfiction. Their relationship in the original series was one of master and servant, but in fanfiction, it can be explored in more complex and romantic ways. Another character often paired with her is Narcissa. Their sisterly bond can be a central focus, or it can be twisted into something more sinister or complex in fan - created stories. Also, sometimes Sirius Black is paired with her in alternate universe stories, given their family connection and the contrast in their loyalties.
Perhaps the biggest plot twist would be Harry's view of the Death Eaters. Growing up with the knowledge that his mother was Bellatrix, he might have a more sympathetic view of some of them at first. He could believe that they were misled rather than inherently evil. This would lead him on a journey to try and reform some of the Death Eaters, which would put him at odds with both the Order and the remaining Death Eaters who don't want to change. It would also change the way we see the divide between good and evil in the wizarding world.
Many fanfics explore the theme of redemption for Bellatrix. They imagine scenarios where she could have turned away from the dark side. Her complex character, with her madness and loyalty, also makes her a great subject for psychological exploration in fanfics.
One idea could be exploring how Bellatrix's pregnancy affects her loyalty to Voldemort. Maybe she starts to question some of his more extreme actions as she thinks about the future for her unborn child.
A really interesting plot could be Bellatrix being given a chance at redemption. In this fanfiction, she could start to question Voldemort's motives after seeing the destruction he causes. She might then try to secretly help the Order of the Phoenix. Also, a plot about her teaching a young Death Eater the ways of the Dark Arts and having second thoughts about it mid - way through could be fascinating.
Some fanfics explore Bellatrix's family relationships more deeply. Like her relationship with Narcissa. There could be a plot where Bellatrix has to choose between loyalty to Voldemort and protecting her sister, which adds a lot of emotional depth.
One big challenge would be trust. Bellatrix has been a loyal Death Eater and has tried to kill Harry many times. Even in pet form, Harry would have a hard time believing she wouldn't turn on him if she regained her normal form. Another challenge would be how others in the wizarding world would react. The Order of the Phoenix might not trust Harry's decision to keep her around, even as a pet.
Well, perhaps Bellatrix discovers a prophecy that involves Harry being crucial for the future of the wizarding world in a way that benefits her own interests in the long run. So, she steps in to save him. It could also be that she has a secret love for Sirius Black (Harry's godfather), and since Harry is related to Sirius, she decides to save Harry out of some twisted sense of loyalty to Sirius.