In this fanfic, Severus's character could develop in a way that he becomes more of a father figure to Harry. After rescuing Harry from the Dursleys, he has to take on a more nurturing role. He might start to teach Harry things that he never thought he would share, like his knowledge of the dark arts in a more controlled and educational way. This would make him grow as a person and also change the way the wizarding community views him.
Severus might start off as just fulfilling a sense of duty. He has always been a complex character. But as he saves Harry from the Dursleys, he begins to see Harry in a new light. He realizes that Harry is not just James Potter's son but an individual with his own struggles. This could lead to him becoming more empathetic towards Harry, gradually shedding some of his cold exterior.
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.
His character could also develop in terms of loyalty. At first, he might be rescuing Harry for some self - serving reasons, like to gain favor with Dumbledore or to stop a threat to the wizarding world that he discovers is related to the Dursleys. But as he spends time with Harry, he could develop a genuine loyalty towards the boy, which is a big shift from his previous animosity.
Perhaps in this fanfic, Severus doesn't just save Harry physically from the Dursleys. He also saves Harry from the emotional and psychological damage that the Dursleys have been inflicting on him. Severus, having his own traumatic past, might be able to relate to Harry on a deeper level and starts to mentor him in ways that Dumbledore never could. This could lead to a completely different Harry, more confident and less impulsive.
In these fanfictions, Snape's character often develops from a seemingly cold and unfeeling person to someone with more depth. When he saves Harry, it starts to chip away at his facade. For example, he might initially save Harry out of obligation but as time goes on, he realizes he has a genuine care for the boy. This is different from his canon behavior where his feelings are mostly hidden.
Severus might be developed as a more complex and empathetic character. By saving Hermione from Ron, he shows a side of himself that is protective and caring, which is different from his usual cold exterior. This could be a turning point in how the other characters view him.
It could be Voldemort. He might have influenced the Dursleys in some way to harm Harry, and Severus has to save Harry from Voldemort's long - reaching plans. For example, Voldemort could have placed a curse on the Dursleys' house that would eventually harm Harry, and Severus discovers it just in time.
In these fanfictions, Severus often develops a more nurturing side. Since he has Harry as a pet, he has to take on a caretaker role, which is different from his usual strict and aloof self. He might become more patient as he guides Harry through various situations.
Severus' character often develops from a cold and aloof figure to a more caring and nurturing one. He starts to open up his heart as he takes on the role of raising Harry. His sense of protectiveness grows, and he becomes more patient, which is a big change from his usual self in the original series.
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.
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.