One thing that could happen is that the wizarding world would be in chaos. The Death Eaters would be confused by Bellatrix's actions, and the Order of the Phoenix would be very suspicious. Harry would be in a difficult position, not knowing whether to trust Bellatrix or not.
If Bellatrix saves Harry from the Dursleys, she might take him to an unexpected location. Maybe she takes him to an old, abandoned Death Eater hideout. There, she could try to train Harry in dark magic, thinking it would make him stronger against Voldemort. But Harry would resist, leading to a battle of wills between them.
In the fanfiction, Bellatrix saving Harry could start a chain of events that changes the whole course of the wizarding war. For example, it could cause Voldemort to doubt Bellatrix's loyalty. This doubt could lead to fractures within the Death Eater ranks. Meanwhile, Harry could use this opportunity to learn more about the Death Eaters' plans from Bellatrix, if he can manage to get her to talk.
In this fanfiction scenario, Bellatrix saving Harry from the Dursleys is quite an unexpected twist. It could be that Bellatrix has some ulterior motive. Maybe she wants to use Harry for her own dark purposes against Voldemort. She might see Harry as a valuable pawn in the power struggle within the Death Eater ranks.
It could be part of a plot where Draco is given an assignment by someone in the wizarding world to save Harry from the Dursleys. He initially does it for self - serving reasons like getting in good with certain powerful wizards who are concerned about Harry's well - being. But during the process, he actually starts to care about Harry.
In some fanfictions, Hermione might use her intelligence and magic skills. For example, she could use a powerful spell to create a distraction at the Dursleys' place. Maybe a spell that makes all the dishes in the kitchen start flying around, causing chaos. Then, while the Dursleys are distracted, she could quickly grab Harry and apparate away to a safe place, like the Burrow or a hidden wizarding location she has prepared in advance.
Charlie might introduce Harry to the dragon world. Since Charlie works with dragons, this could be an exciting new adventure for Harry. It would also give him a new perspective on the magical world and something to focus on other than his difficult past with the Dursleys.
One possible plot could be that Voldemort realizes Harry's importance in a different way. Maybe he sees that Harry has some power or knowledge that could be useful to him in the long run. So, instead of wanting to kill Harry, he decides to rescue him from the Dursleys to gain his trust and manipulate him later. For example, Voldemort might think that Harry has a connection to some ancient magic that only he can access, and by saving him, he hopes to get access to it through Harry.
Well, perhaps Fleur uses her Veela charm to intimidate the Dursleys into letting Harry go. She could arrive at Privet Drive in a blaze of magical beauty and power, and the Dursleys, being the cowards they are, would be too scared to oppose her when she demands Harry come with her.
The Dursleys might be left in a state of shock and confusion. Since they have been so mean to Harry, they could be worried that the wizarding world will come after them for revenge. But since they are Muggles, the wizarding world may just leave them be, but they will always live in fear of the unknown.
It could be that Daphne has a personal connection to Harry that she's not aware of until she starts investigating the strange magical disturbances around the Dursleys' place. Once she realizes it's Harry in trouble, she enlists the help of her friends or some sympathetic wizards to break Harry free. She might also face some challenges along the way, like dealing with the Dursleys' resistance or the Ministry of Magic's rules about interfering in Muggle affairs.
In the fanfic, Bellatrix might use her magic to protect Harry from his abusers. Maybe she realizes the wrongness of the abuse and decides to be his unexpected savior. She could use her dark magic skills to intimidate those who harm Harry, creating a sort of dark - but effective - protection around him.
Well, perhaps Daphne somehow discovers Harry's awful situation at the Dursleys. She might use magic to break into the house secretly. Then she could use a spell to make the Dursleys forget about Harry so that she can take him away without a fuss.