It could be Sirius Black. Sirius is Harry's godfather and he is very protective of Harry. He might break out of his confinement (if he is still in that situation in the fan fiction) and rush to Vernon's house. Sirius has the skills and the determination to face Vernon and save Harry. He could transform into his Animagus form, a large black dog, and intimidate Vernon into letting Harry go.
Maybe Dumbledore steps in at the last moment and takes Harry away from Vernon's house. He could use his powerful magic to protect Harry and remove him from that hostile environment.
Dudley might face his father's anger. Vernon could be furious that Dudley has gone against him to protect Harry.
In this fan fiction scenario, Snape might use his knowledge of the Muggle world and Vernon's weaknesses. Snape could have found out some information about Vernon's business affairs or personal secrets. Then he blackmails Vernon into leaving Harry alone. By doing this, he effectively saves Harry from Vernon without having to use too much magic and draw unwanted attention.
It could be that Snape wants to spite Vernon. Vernon represents everything that Snape despises about Muggles who are cruel and unaccepting. By saving Harry from Vernon, Snape is showing his superiority over Vernon and also his power as a wizard. And of course, there's still that underlying reason of his love for Lily which makes him want to protect her son.
Perhaps Dudley finally stands up to his father's cruel treatment of Harry. Maybe he realizes that Vernon's behavior towards Harry is wrong and uses his own physical strength or some clever ruse to get Harry out of a difficult situation Vernon has put him in.
Maybe Voldemort uses his magic to stun Vernon first. Then he could simply apparate with Harry to a safe place.
In this type of fanfiction, Snape could simply intimidate Vernon. Snape has an air of mystery and a certain power about him. He might show up at Vernon's doorstep, give Vernon a cold stare, and with his reputation as a powerful wizard, Vernon might be too scared to oppose him. Snape could then just take Harry without much resistance from Vernon.
Petunia could be a great addition. Her relationship with both Harry and Vernon adds a lot of complexity. She could be the mediator or the one causing more trouble between them, depending on the plot.
Perhaps Voldemort has a change of heart. He realizes that Harry has some value to him alive other than just being his enemy.
Well, in some fanfics, Voldemort might have his Death Eaters spying on the Dursleys. So they could've reported Harry's location to him. Another possibility is that Voldemort has some sort of dark magic tracking device on Harry that led him there.