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.
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.
The main characters are Dudley and Harry. Dudley, who has usually been portrayed as a bully in the original series, is now the hero. Harry, on the other hand, is the target of whatever danger is present in the fanfiction. There might also be other supporting characters like Dudley's parents or some of Harry's friends from Hogwarts who could play a role in the story.
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.
One possible plot point could be Dudley finally realizing the true nature of the danger Harry is in and using his new - found courage to save him. Maybe he discovers some secret about Voldemort that helps him protect Harry. Another could be Dudley using his physical strength, which he was known for in the original series in a more heroic way to fend off Death Eaters.
Another idea for a 'Harry Saves Vernon' fanfic could be set during a time when the wizarding world is under attack and the protection spells around the Dursleys' house fail. Harry, who has a sense of duty towards his aunt and uncle despite their past treatment of him, comes back to save Vernon from the invading dark forces. He might use his Patronus charm to drive away Dementors or use defensive spells to fend off Death Eaters who are targeting the Muggles in Little Whinging.
You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own (AO3). Just use the search function and type in 'Harry Saves Vernon' and you should get a list of relevant fanfics.
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.
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.