Well, in some fanfic scenarios, Voldemort might have made a deal with someone who has access to the Dursleys' house. For example, he could have bribed or threatened a neighbor or someone who works in the area. Then, when the time is right, he enters the house under the guise of this person's help and rescues Harry. It could also be that Voldemort has some sort of inside knowledge about the protective spells around the Dursleys' place. He finds a loophole in those spells and slips in to save Harry.
Another reason could be that Harry in the fanfic has a newfound sense of self - worth. He realizes he doesn't deserve the horrible treatment from the Dursleys and decides to break free. He may have learned about his true heritage in a different way in the fanfic and decides to leave behind the Dursleys, who have always tried to suppress his wizarding identity.
Perhaps Snape uses magic to create a distraction at the Dursleys' place. He could make strange noises or apparitions that scare the Dursleys, and while they are in a panic, he grabs Harry and disapparates. This would be a quick and efficient way for him to rescue Harry.
In a Naruto fanfic where Naruto runs away from Kushina, it could be due to various reasons. Maybe he feels misunderstood. For example, Kushina might be too strict with him in the fanfic's storyline, not allowing him to pursue his own ninja way freely, so he decides to run away to find his own path and prove himself.
There's also 'Finding Freedom on the Run'. This fanfic delves deep into Harry's emotions as he runs away. He encounters various characters who help him understand his true potential. It has a great plot that keeps you hooked from start to finish. The author does an amazing job of portraying Harry's journey of self - discovery.
Maybe Harry runs away to America to escape the dangerous wizarding world in the UK. He could start a new life in America, perhaps meet new friends who are different from those in Hogwarts, and learn about American magic. He might also be hiding from some dark force that was after him in the UK.
Well, maybe Harry runs away to Canada because he's tired of the drama in his home country. He could be seeking a new start, away from all the chaos. In Canada, he might meet new friends who help him discover a whole new side of himself.
Hermione could be one of the main characters. She might be the one who tries to find Harry and bring him back. She would use her intelligence and knowledge of magic to track him down, all while worrying about his safety.
Maybe he gets help from his friends. For example, Ron and Hermione could come up with a plan. They might send him a magical object that can help him escape, like a flying broomstick that he can use to fly away from the Dursleys' house without being noticed.