In some fanfics, he might be saved by his latent magic power that suddenly bursts out when he is in extreme danger. For example, it could create a protective shield to fend off the Dursleys' attacks.
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.
Maybe Percy uses his magic skills to create a distraction. He could conjure up some strange creatures outside the Dursleys' house. The Dursleys, being afraid of all things magical, would be distracted long enough for Percy to sneak in and get Harry out.
Jealousy could be one motive. They might be jealous of Harry's special status as a wizard. They see him as different and a threat to their 'normal' family life, so they want to get rid of him.
Another character could come to his rescue. For instance, Sasuke might show up at the crucial moment. Despite their complex relationship, Sasuke still values Naruto as a friend or rival. He intervenes and stops Sakura from killing Naruto. Or perhaps Kakashi, Naruto's teacher, arrives in time. He uses his Sharingan or some other jutsu to neutralize Sakura's attack and save Naruto.
The abuse makes Harry more cautious. He has learned from the Dursleys that the world can be cruel, so he's careful about who he trusts. For example, he might be hesitant to open up to new people he meets at Hogwarts.
In this fanfic, the Dursleys may be depicted as being in over their heads. Vernon Dursley, for example, might be shown as constantly angry and trying to assert his authority in a situation where he has none. Petunia Dursley could be portrayed as being torn between her dislike for magic and her sense of family obligation towards Harry. Dudley might be shown as being bullied or affected in the Muggle world because of Harry's presence in their family.
Harry's character might grow in resilience. The neglect forces him to become self - reliant. He has to fend for himself, which makes him tougher. For example, he learns to cook his own meals and take care of his basic needs without any help. This self - sufficiency builds his confidence over time.
It might show the constant power struggle between them. Harry, as a wizard, has an inner strength that the Dursleys try to suppress with their mundane and cruel ways. So it's a battle of wills.
It might show their fear in a more extreme way. Instead of just being dismissive of magic, they could be absolutely terrified of it. For example, every time Harry does something even slightly magical, they could cower in a corner.
Well, in some fanfics, Harry might show extraordinary magical abilities early on. For example, he could have a natural talent for advanced spells that are usually taught in higher grades. Maybe he aces all his exams with flying colors and the professors recognize his potential and allow him to skip grades.