Well, one possibility could be that Draco has a change of heart. Maybe he realizes the unfairness of Harry's situation at the Dursleys'. He could use his family's influence or some magic skills he has to get Harry out. For example, he might create a diversion to distract the Dursleys while he sneaks Harry away.
Well, it could be that Draco has a change of heart early on. He realizes that the Dursleys are truly awful to Harry. So he uses magic to create distractions. He could make strange things happen around the house that scare the Dursleys so much that they just want Harry to leave. Then Draco could be waiting outside and whisk Harry away to a safer place, like a hidden place in the wizarding world where he has set up a little haven for Harry.
Maybe Draco finally understands that Harry is a victim of circumstances. The Dursleys' treatment of Harry is cruel, and Draco, having grown up in the wizarding world, realizes it's wrong. So he steps in to rescue Harry.
The plot twist could be related to Snape's true motives. He might be under an Unbreakable Vow to rescue Harry from the Dursleys. In the process, Harry realizes that Snape is not as bad as he seems. This could lead to a complete change in their relationship. Harry could start to trust Snape, and Snape, in turn, could teach Harry some unique magic that he has never learned before, which is crucial for the upcoming battle against Voldemort.
Perhaps Snape discovers some dark plot involving the Dursleys that could harm Harry more than he initially thought. The Dursleys were known to be cruel to Harry, and Snape might have found out that they were involved with some Death Eaters or dark magic users who planned to use Harry in a harmful way. So, he decides to rescue Harry to prevent this from happening.
At first, Harry might be extremely suspicious. Snape has always been cold and mean to him in the past. He would wonder what Snape's true motives are. Harry is used to being on his own and not relying on Snape for help, so this sudden rescue would be very unexpected.
He could be doing it out of a sense of justice. Despite his family's views, Draco might see that the way the Dursleys treat Harry is wrong and decides to step in.
It could be part of a plot where Draco is given an assignment by someone in the wizarding world to save Harry from the Dursleys. He initially does it for self - serving reasons like getting in good with certain powerful wizards who are concerned about Harry's well - being. But during the process, he actually starts to care about Harry.
The wizarding world would be in shock. The Malfoys are known for their dislike of the Potters, so Draco saving Harry would go against the family's reputation. It could lead to Draco being ostracized by some in the pure - blood community.
Perhaps Severus, while rescuing Harry, stumbles upon a hidden connection between the Dursleys and the Death Eaters. This would add a whole new layer of danger and mystery. He might have to fight off some of his former allies to get Harry to safety. It could also lead to a change in Severus' perception of Harry as he realizes the boy has been in more danger all along than just from Voldemort.