Well, perhaps in this fanfic, Harry notices Draco in a dangerous situation with Buckbeak. Maybe Draco was taunting Buckbeak and it got out of hand. Harry, being the brave one, steps in and uses his skills with magical creatures to calm Buckbeak down just in time to save Draco from getting seriously hurt.
In a romance fanfic scenario, Draco could save Harry from Dumbledore if there is some sort of misunderstanding. Dumbledore might be acting on information that Draco knows is false. Since Draco has fallen for Harry, he steps in to prevent harm. For example, Dumbledore could be about to send Harry on a dangerous mission that Draco knows is a trap. Draco's love for Harry makes him take a stand against Dumbledore.
One common theme is redemption. Harry saving Draco can be seen as a way for Draco to start on a path of redemption from his previous actions as a Slytherin. It gives him a chance to change.
Another one could be 'When Draco Saved Harry'. It might show a scenario where Draco saves Harry from a cursed object in Hogwarts. This fanfic could explore how the other students react to this unexpected turn of events, and how Draco and Harry start to see each other in a different light.
The theme of self - discovery is also prevalent. Draco might discover new aspects of himself, like his capacity for good or his true feelings towards Harry through the act of saving him. It can be a journey of him realizing that he doesn't have to follow the path that was set for him by his family or the Slytherin stereotype.
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.
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.
One popular 'harry saves draco fanfiction' is 'The Green Light'. In this story, Harry discovers Draco in a dangerous situation in the Forbidden Forest and uses his magic to save him. It's a great read for those who like the idea of their dynamic changing from rivalry to something more.
It allows for character development. Draco gets to be more than just the school bully. Saving Harry gives him a chance to redeem himself and show his good side. And for Harry, it makes him see Draco in a new way. This creates a whole new set of interactions and emotions that fans enjoy exploring in fanfiction.
There's also 'Draco's Redemption' which features Draco saving Harry during a dangerous encounter with dark wizards. In this fic, it shows Draco's character development that leads him to make the heroic move of saving Harry. The story also delves into the complex relationship between the two characters afterwards, exploring how they deal with the new dynamic. It's a great read for those who love the idea of Draco being the one to come to Harry's aid.