In some fanfictions, Bellatrix might save Harry because she is magically bound to him in some way. Maybe a spell backfired and now she has to protect him. Or perhaps she has a secret love for Sirius Black (Harry's godfather) and in order to honor his memory, she saves Harry. There could also be a plotline where Bellatrix is tired of Voldemort's tyranny and sees Harry as the one who can overthrow him, so she saves him for the greater good of the wizarding community.
One popular 'Bellatrix Saves Harry' fanfiction might be on platforms like FanFiction.net or Archive of Our Own. You can search using those keywords on the sites to find relevant stories. Some stories might explore an alternate universe where Bellatrix has a change of heart and decides to save Harry for various reasons, such as a newfound sense of morality or a prophecy she interprets differently.
One possible plotline could be that Harry uses a powerful spell he's been secretly practicing to stun Bellatrix just in time as she's about to harm Hermione. For example, he might use a modified version of the Stupefy spell that's more powerful. Another could be that Harry manages to create a diversion, like summoning a horde of magical creatures, which distracts Bellatrix long enough for him to rescue Hermione.
It could be that a powerful sorcerer in the Avengers' world goes rogue and starts using dark magic. The Avengers don't know how to handle magic, so Harry is called in. He has to face this rogue sorcerer, using his own brand of light magic. Along the way, he might have some clashes with the Avengers' way of doing things, but in the end, they all work together and Harry manages to save the day by defeating the rogue sorcerer and restoring peace in the Avengers' world.
A plotline could involve Petunia having a change of heart due to a magical event. For instance, she might accidentally stumble upon some of Harry's magic or receive a message from the wizarding world about his importance. This could lead her to stand up against Vernon and protect Harry. She could then start to teach Harry about his mother's side of the family and the magic that runs in his veins in a more positive way than the Dursleys ever did. And perhaps she even helps him develop his magic skills secretly before he goes to Hogwarts.
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.
One highly recommended fanfiction is 'The Unlikely Savior' which really delves into Bellatrix's complex motives for saving Hermione. It has great character development and a very engaging plot.
One possible plotline is that Harry is magically transported to the Naruto world and discovers Naruto is in danger from a new, powerful enemy. Harry then uses his magic to fight alongside Naruto and his friends, saving Naruto in the process.
One possible plotline could be that Voldemort discovers Harry's abuse through his Death Eaters' spying. He decides to save Harry as he wants to turn Harry to his side and believes that by rescuing him, Harry will be more likely to join him. Another could be that Voldemort has a moment of self - reflection and realizes that the way Harry is being treated is wrong, so he steps in.
One possible plotline could be that Amelia Bones discovers a plot against Harry before it's too late. Maybe she uncovers some dark wizard's plan to harm Harry at Hogwarts and uses her position in the Ministry of Magic to protect him. For example, she could assign extra guards to the school or personally investigate any threats.