One scenario could be that a powerful magic spell backfires and turns Bellatrix into a small animal that Harry then takes in as a pet. Another could be that in an alternate universe created in the fanfiction, the power dynamics are so different that Bellatrix is somehow subjugated to Harry and made into his pet.
A possible plotline could start with Bellatrix having a strange fascination with Harry from the start. She manages to get him in her clutches and treats him like a pet. Harry, on the other hand, uses his wits and the limited magic he can access in this state to outsmart Bellatrix. There could be a lot of psychological battles between them, with Harry trying to understand Bellatrix's twisted mind while she tries to break his spirit. And all this could be set against the backdrop of the ongoing war between the good and the evil in the wizarding world.
One possible plotline could be that Bellatrix captures Harry during one of his adventures and decides to keep him as a pet for her own amusement. She might use dark magic to bind him and make him obey her commands. Another could be that in an alternate reality, Harry is somehow magically enslaved to Bellatrix from the start, and the story follows his attempts to break free from her control while she uses him for various dark purposes, like spying on the Order of the Phoenix.
Well, it depends on the specific fanfiction. There are countless fanfictions out there with all kinds of strange and wonderful ideas. Some might indeed depict Bellatrix as Harry's pet. It could be a part of a plot where magic or some other factor has changed their relationship completely. For example, a spell gone wrong or a new magic system introduced in the fanfic could lead to such an odd relationship.
In a more complex scenario, Bellatrix could be trying to use a dark magic ritual that would cause great harm to the wizarding world. Harry discovers her plan and has to engage her in a magical struggle. In the process, he manages to turn her own dark magic against her, which results in her death. This would show Harry's ingenuity and his ability to use the enemy's own weapons against them.
One possible scenario is that Snape steps in during a confrontation. Bellatrix is about to harm Hermione, and Snape, using his quick reflexes and advanced magic, stops her. He could be acting out of his own sense of right and wrong, or perhaps because he has a hidden agenda that involves keeping Hermione safe.
Perhaps in the fanfiction, Bellatrix stabs Hermione as a way to get to Harry Potter. She might think that by harming Hermione, she can draw Harry out and into a trap. Hermione is one of Harry's closest friends, so this would be a strategic move on Bellatrix's part.
Well, it would be very strange. Bellatrix is a Death Eater and Harry is her enemy in the original story. In this kind of fanfiction, perhaps Bellatrix would keep Harry captive in some way and treat him like a pet, which is quite a dark and twisted concept.
Well, for one, it goes against the spirit of the Harry Potter universe. The series is about magic, friendship, and the fight against evil. This kind of fanfiction concept takes it into a very dark and inappropriate realm. Also, it can be seen as objectifying Bellatrix in a very wrong way, reducing her to a mere 'pet' which is not only disrespectful to her character but also to the readers who have an understanding of the complex character she is in the original work.
One possible plotline could be that Harry discovers the truth slowly. At first, he might notice strange similarities between himself and Bellatrix or some unexplained magical abilities that seem to link him to her. This discovery could throw him into an identity crisis as he has always thought of himself as an orphan with no real family other than the Dursleys.
Maybe it was a last - minute decision by James and Lily. They might have thought that having Bellatrix as a godmother would offer some kind of protection. After all, she was a powerful witch. Or perhaps there was some sort of old family pact or agreement that made her the godmother.