In this fan fiction, Harry might save Severus through some form of unique bond. It could be an emotional bond where Harry realizes Severus's hidden goodness or a magical bond that gives him the power to rescue Severus from a dangerous situation, like a dark spell or a life - threatening attack from Voldemort's side.
It could be that Harry, through his kind heart, comes to understand Severus's complex past and motives. He realizes that Severus is not all bad and that there is a deeper connection between them. This new - found understanding and emotional bond drives Harry to save Severus from harm.
In the fan fiction, Severus could start to develop a sense of responsibility towards Harry. At first, he may have saved Harry out of a sense of duty to Lily Potter, but as time goes on, he realizes that Harry has his own worth. This could make him more open to forming a bond with Harry, which is a huge change for his character who has been so closed - off for so long. He may also start to question some of his long - held beliefs about the Gryffindors, especially as he sees Harry's courage in the face of his difficult upbringing at the Dursleys.
Obviously, Severus Snape and Harry Potter are the main characters. Severus is the one doing the saving, and Harry is the one being saved from the Dursleys. But there could also be other characters involved. For example, Dumbledore might make an appearance. He could either support Severus's actions or be a bit wary of them. Petunia Dursley could also be a significant character as she is part of the reason Harry needs to be saved from that household.
One common theme is redemption. Snape's actions to save Harry are often seen as a way for him to atone for his past mistakes or his association with the Death Eaters. It gives him a chance to be a hero in his own right.
Maybe Severus discovers some dark magic plot that involves the Dursleys harming Harry in a more serious way. So, he intervenes just in time. He could use his skills in potions and magic to subdue the Dursleys if they resist, and then take Harry to a safe place, like his own secret hideout or a friendly wizard's home.
Well, perhaps when he directly confronts Voldemort to protect Harry. He might use his powerful magic skills that Voldemort doesn't expect, like some unique spells he has been secretly practicing. This moment shows his courage and his determination to save Harry at all costs.
He might use his skills in Legilimency. By probing the minds of Voldemort's followers or looking into the general 'aura' of the area where he suspects Harry to be. This way, he can get a sense of Harry's location even if it's well - hidden.
In some fan fictions, Severus might save Harry from the Dursleys because he realizes that Harry is the key to defeating Voldemort in the long run. He might see that the Dursleys' treatment is making Harry weak and less likely to be able to face Voldemort. So, he intervenes, maybe by intimidating the Dursleys into treating Harry better and providing him with proper education about the wizarding world. He could also give Harry some potions to boost his health and magical abilities that have been stunted by the Dursleys' neglect.
Well, perhaps in the fan fiction, Severus saves Harry from the Dursleys but then has to deal with the consequences of going against Dumbledore's plan. Dumbledore might have had a reason for leaving Harry with the Dursleys, and Severus' actions could set off a chain of events that changes the whole wizarding world. Also, Severus could find out that the Dursleys were part of a much larger conspiracy against the wizarding world, and by saving Harry, he uncovers this plot.