In some fanfictions, magical creatures play a role in saving Harry. For instance, a friendly house - elf might find out about Harry's situation and use their magic to transport him to a safe place. Also, it could be that a centaur, known for their wisdom, senses Harry's distress and comes to his rescue. The centaur could use their knowledge of magic and the forest to hide Harry from the Dursleys.
One way could be through the intervention of a powerful wizard or witch who discovers Harry's mistreatment. For example, Dumbledore could send someone like Sirius Black earlier to rescue Harry. Another way might be if Harry himself discovers his magic earlier and uses it to escape. Maybe he finds a magical object in the Dursleys' house that helps him get away from their cruelty.
Hermione Granger could also be a rescuer. She was always intelligent and resourceful. In a fanfiction, she might figure out that Harry was in danger at the Dursleys' through some research or a hunch. Then she could use her knowledge of magic to break into the Dursleys' house and get Harry out. She would be brave enough to take on such a task to save her friend.
There are fanfictions where a powerful wizard or witch, not part of the main Hogwarts faculty, discovers Harry's situation. Maybe an old hermit wizard who lives on the outskirts of the wizarding world. This wizard uses his magic to create a diversion at the Dursleys' place and then whisks Harry away to his own hidden cottage where he teaches Harry different kinds of magic not taught at Hogwarts.
One popular 'Harry Potter Saved from Dursleys' fanfic could be 'The Early Rescue'. In this fic, perhaps a powerful wizard discovers Harry's situation much earlier and takes him away from the Dursleys. Another might be 'A Different Start' where a magical creature intervenes and whisks Harry to a safe place away from his cruel relatives. There could also be 'Saved by the Unlikely' where a Muggle with some latent magical ability stumbles upon Harry and saves him from the Dursleys.
There are quite a few. One popular one is 'The Protector's Grace' where a powerful wizard steps in to rescue Harry from his miserable life with the Dursleys.
In this kind of fanfiction, perhaps Harry is rescued by the Order of the Phoenix earlier than in the original story. They might have realized the Dursleys' mistreatment sooner. Then Harry could start his magical training earlier, away from the hostile environment of the Dursleys' home. He may also form closer bonds with other members of the Order, like Sirius, who could play a more active role in his upbringing.
Perhaps in the fanfic, a time - traveling wizard goes back to save Harry from the Dursleys. This would lead to a lot of changes in the timeline. Harry might be introduced to magic much earlier and form different relationships. He could also have a different understanding of his parents' history and his own role in the wizarding world as a result of being removed from the Dursleys' environment.
Well, the Dursleys were really horrible to Harry. Fans want to see different ways he could have been saved. It also allows for new storylines. For example, if he's saved early, how would his magical development be different? How would his relationships with other characters change? All these possibilities make these fanfics interesting. Also, it gives a chance to explore different magical elements and characters in the context of rescuing Harry from the Dursleys.
One common reason is the abuse he endures at the Dursleys'. The writers feel that Harry should not have to put up with such a horrible family. So they create scenarios where he is saved, often by magical creatures or other wizards who can't stand to see a child so mistreated.
Hermione could be the rescuer. Maybe she discovers through her research that Harry is in a bad situation at the Dursleys' and decides to take action. She uses her intelligence and magic skills to break into the Dursleys' house and get Harry out. Then they would go on an adventure together, and Hermione would be like a mentor to Harry in a way, teaching him things she has learned from books.
In some more extreme fanfiction scenarios, she might use a magical object like a broomstick to swat at Harry. However, this would be a very out - of - character action for Molly in most cases, but in the realm of fanfiction where creativity runs wild, it could be a possibility. She would probably only do this if she was extremely angry and felt that Harry had really crossed a line, like endangering one of her children's lives in a really stupid way.