The relationship would be drastically different. Harry, who has always seen Snape as a rather unlikable figure, would start to see him in a new light. He might come to respect Snape as a father figure. Draco, who has some connection to Snape through his family, would now have a more personal and perhaps more positive relationship with Snape. Snape himself would have to soften his usual harsh demeanor towards Harry. And between Harry and Draco, they would be forced to get along better as they are now under the same roof. They might start to understand each other's insecurities and backgrounds more.
If Snape adopts them in a fanfic, for Harry, it would be a huge shift. He has long been at odds with Snape, but now Snape is his guardian. This could lead to Harry trying to figure out Snape's true nature. For Draco, Snape would be a strict but fair parental figure. He would likely enforce rules that Draco isn't used to from his own family. As for Snape, he would have to deal with the two boys' different personalities. Harry is brave and impulsive, while Draco is more cautious and proud. Snape would need to mediate between them when they clash, and in the process, all three of them would grow closer. They might start to share their secrets and fears, forming a unique bond that was unthinkable before.
They would probably become like brothers. With Snape as their common father figure, they would have to learn to get along. Harry might be more forgiving of Draco's past actions, and Draco would have to let go of his animosity towards Harry.
In the fanfiction, their relationship would be complex at the start. Snape, having his own demons and secrets, would be a bit of an enigma to Draco. Draco, on the other hand, would be dealing with the loss of his family's status. Snape would start by providing a stable home for Draco. As they interact more, Draco would notice Snape's small acts of kindness. Snape would encourage Draco to explore his own identity outside of the Malfoy name. This would lead to a closer relationship, with Snape teaching Draco about things like loyalty, sacrifice, and the true nature of magic, and Draco in turn bringing out a more human side of Snape.
The relationship would start off rocky. Snape would be resistant to Harry's kindness as he has always seen Harry as James Potter's son. But Harry's persistent efforts to understand and help Snape would gradually break down Snape's walls.
One possible plot could be that Snape, seeing the troubled situations of both Harry and Draco, decides to take them under his wing. He could start by teaching them more advanced magic in a strict but fair way. Harry might initially be resistant as he has his own ideas about Snape, but gradually realizes Snape's good intentions. Draco, on the other hand, might struggle with the idea of being under Snape's authority as he is used to his family's influence. They could all learn to live together, with Snape guiding them through the challenges of Hogwarts and the wizarding world at large.
It could change in a more positive way. In detention, they might have to rely on each other to get through Snape's tasks. If they are made to work on a complex magical experiment, they would need to communicate. This communication could break down some of the barriers between them. Maybe they start to exchange a few friendly words outside of detention, slowly building a more amicable relationship.
The relationship would be a rocky one. Snape has his past grudges against Harry's father. However, living together, they would be forced to interact daily. Harry might start to understand Snape's difficult past and Snape could see Harry's potential. There could be moments of anger, but also moments of mutual understanding, like when Harry helps Snape with some magical experiment.
Snape would likely become more nurturing. Instead of just being the strict and often cold Potions master, he would have to show a softer side to take care of Harry. He might be more patient as he guides Harry through his magical education and daily life.
In a fanfiction scenario, Harry's actions could cause a complete breakdown in any potential for a positive relationship between them. Snape's loyalty to Dumbledore and his role in protecting Harry from the shadows would be put at risk. Harry would have to face the fact that he may have made a huge mistake. And Snape, who has sacrificed so much already, would be in an even more precarious position, both with Voldemort and in the wizarding world in general. This could lead to a chain of events that completely alters the course of the wizarding war, with far - reaching consequences for both Harry and Snape.
The relationship would become extremely strained. Harry would likely go from having some level of respect or at least tolerance for Snape to feeling intense hatred. He might avoid Snape at all costs and even start to plot revenge in his head.
At first, it's likely to be tense. Harry has years of seeing Snape as a bully. But as they start living together, they begin to understand each other. Snape might show his more vulnerable side to Harry, like his memories of Harry's mother. Harry, in turn, starts to respect Snape's knowledge and sacrifice. Eventually, they develop a bond like a father - son relationship.