snape saves harry from his parents fanfiction

Well, it could become more positive. Harry might grow up seeing Snape as a hero or a protector, instead of the antagonist he was in the original story. This would lead to a more trusting relationship between them.

Maybe Snape has some sort of premonition or knowledge that Harry is going to be crucial in the fight against dark forces in the future. So, in order to ensure that future, he steps in to save Harry from whatever danger his parents' situation might put him in. He might also be trying to atone for past mistakes or grudges he held against Harry's father by protecting his son.

The Dursleys might be left in a state of shock and confusion. Since they have been so mean to Harry, they could be worried that the wizarding world will come after them for revenge. But since they are Muggles, the wizarding world may just leave them be, but they will always live in fear of the unknown.

In fanfiction, Snape saving Harry often showcases a complex side of Snape's character. It might be a redemption arc for him, as in the original series, Snape had a very ambiguous relationship with Harry. In these fanfictions, it could be due to his love for Lily that he finally decides to fully protect Harry, which is a very interesting take on his character.

One motivation could be Snape's sense of duty as a teacher. Despite his dislike for Harry in some ways, he still has an obligation to protect the students. So, when he sees Lockhart endangering Harry, he steps in.

Another possibility is that Snape uses his position as a teacher. He might threaten Lockhart with the consequences of harming a student. Given Snape's intimidating presence and his own power within the school, Lockhart would be afraid to cross him. Snape could also call for other teachers to help, making it clear that he won't let Lockhart get away with any harm to Harry.

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 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.

They might face magical justice. In some fanfictions, the Ministry of Magic could get involved and strip them of their magic, or at least put them under strict surveillance.

Well, he could use his magic skills secretly. Maybe he casts a spell on the Dursleys to make them docile or distracted long enough to get Harry out. For example, he might use a Confundus Charm on them so they don't notice Harry leaving.