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.
Sirius may simply be acting out of his own moral code. He has seen the harm that Lucius can do, and he doesn't want an innocent, even if that innocent is from a family like the Malfoys, to be a victim of Lucius' cruelty. He might also think that by saving Draco, he can change Draco's future and perhaps turn him away from the dark path that Lucius is leading him down.
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.
One motivation could be self - preservation. Draco might realize that if Voldemort kills Harry, it will lead to an all - out war that could destroy everything he knows. By saving Harry, he hopes to find a more peaceful solution and protect his own family and the wizarding world in a broader sense.
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.
Obviously, Lucius could be the main antagonist here as he is the one starving Draco. His actions are harmful to Draco and go against basic care for a family member.
Simple. Naruto is a hero at heart. He can't stand seeing anyone being hurt, especially his friends. Ino is his friend, so he has to save her from Sasuke.
Draco might be motivated by jealousy. He could be jealous of Ron and Hermione's friendship or a possible romantic relationship between them. So he tries to harm Hermione out of spite.
Harry Potter can be an interesting character to pair with them. It creates a lot of conflict and potential for character development. Given their opposing stances in the original story, it can lead to some really intense and thought - provoking scenarios in fanfiction.
Love for Lily. Since Harry is Lily's son, Snape might feel an obligation to protect him. He couldn't save Lily, but he can try to keep her son safe.
Eric might also see Tris as an asset to his own plans or goals. If he wants to gain more power or influence within their community, he might think that by saving Tris from Peter, he can earn her loyalty and have her on his side. And Tris is known for her strong will and skills, which can be useful to Eric.
Well, usually it leads to some intense drama and conflict. Maybe Draco gets scolded or given some important instructions.