In many such fanfictions, Sirius might use his magic skills. He could be quicker and more powerful than Lucius in a duel. Maybe he uses a powerful spell to stun Lucius and then whisks Draco away to safety.
Well, Sirius is a brave and resourceful character. It could be that he has some prior knowledge about Lucius' plan to harm Draco. He might have set up a trap for Lucius. When Lucius is distracted by the trap, Sirius grabs Draco and disapparates them to a safe location. He also might have some help from his friends, like he gets Remus to create a diversion while he rescues Draco.
In this fanfiction, Harry might also save Draco by appealing to Lucius' sense of self - preservation or family. He could threaten to expose some of Lucius' secrets or illegal activities if he doesn't let Draco go. Or, if there is some underlying family drama involved, Harry could use that to his advantage. For instance, if there's a feud within the Malfoy family that Harry is aware of, he could manipulate the situation in a way that makes Lucius back off and leave Draco unharmed.
Sirius might see Draco as just a young boy being influenced by a bad father. He could have a sense of wanting to protect the innocent, regardless of which side they seem to be on. So he steps in to save Draco from Lucius' potentially harmful actions.
Well, perhaps he uses his influence in the wizarding world. Maybe he has some connections or knowledge that allows him to intervene and get Hermione out of the abusive situation. For example, he could use his status among the pure - blood families to put pressure on the abusers.
Well, in some fanfictions, Lucius might use his charm and power. He could be depicted as very persuasive and use his status in the wizarding world to make Hermione see him in a different light. Maybe he offers her opportunities for knowledge or power that she doesn't get with Draco.
Well, it could be that Lucius uses his powerful influence in the wizarding world. Maybe he intimidates Ron with threats related to his family's status or he uses some dark magic to create a distraction and whisk Hermione away.
In some versions, Hermione might use her advanced magic knowledge. She could have discovered a spell that counteracts the pull of the veil. Maybe she found a way to disrupt the dark magic associated with it and was able to pull Sirius back from the brink just in time.
Well, perhaps Harry uses his quick thinking and his knowledge of magical creatures. He might step in just in time, using a spell to distract Buckbeak before it can harm Draco. For example, he could use a simple levitation spell to lift a small object and draw Buckbeak's attention away from Draco.
Snape, being a skilled wizard, could use magic to protect Draco. He might cast protective spells around Draco when he's alone or in vulnerable situations. Maybe he uses a spell that alerts him whenever Draco is in danger, so he can rush to his aid immediately.
Well, it changes Draco in many ways. Firstly, he realizes that there are things more important than loyalty to his family's dark cause. Saving Hermione makes him see the goodness in people like her. It could also make him more determined to change the reputation of his family. He may start to work secretly against the Death Eaters, using his knowledge of their plans from being part of the Malfoy family. His relationship with Hermione could also be a catalyst for his character growth, as she challenges him intellectually and morally, pushing him to become a better person.
Well, perhaps Snape uses his position as a teacher to step in. He could have been observing the situation secretly and when Draco was about to do something harmful to Hermione, Snape intervened with a firm command or some magic spell to stop Draco in his tracks.