They might choose to run away because they want privacy. After all the battles and saving the world multiple times, they just want some time alone without any interruptions from other demigods or the gods. So running away seems like a good option.
Perhaps they run away because they are tired of all the rules and expectations placed on them. They just want to be free and explore the world on their own terms. They could end up in a small, idyllic town where they learn more about normal human life and each other away from the chaos of the demigod realm.
One reason could be to avoid a dangerous prophecy that they believe the camp can't protect them from. In some fanfictions, they might think that by running away, they can face the threat on their own terms.
He could run away because he feels pressured. When he meets Annabeth, it's important because she can offer him support and guidance. In fanfiction, their meeting can lead to many different plot developments. For instance, they might go on a quest to find a lost artifact that has the power to change their world. Annabeth's knowledge and Percy's courage will be crucial in this journey.
He could run away to a far - off wizarding village. There are many small, secluded villages in the wizarding world that are not well - known. For example, a place like Hogsmeade but much more remote, where he can start anew and not be bothered by his past or family.
Percy's impulsive nature can be both a strength and a weakness. His quick decisions can sometimes get them out of immediate danger, like when he suddenly decides to charge at a group of monsters to create a distraction. Annabeth, on the other hand, is more calculating. She can rein in Percy's impulsiveness and make sure their plans are well - thought - out. For example, when they need to infiltrate a heavily guarded place, she'll come up with a detailed strategy and Percy will be the one to execute the more dangerous parts with his combat skills.
Draco's character could develop from a somewhat arrogant and prejudiced boy to a more empathetic and self - aware person. Being with Hermione, who constantly challenges him intellectually and morally, would force him to grow. Hermione would also develop in terms of her relationships. She would learn to trust someone from a different background and perhaps become more rebellious against the norms of the wizarding society that have been holding her back in some ways.
Perhaps they are tired of the constant power struggles and drama. Bella has seen a lot of chaos in the vampire world, and Jasper has been through it for a long time. Together, they decide to run away to find some peace. They want a life away from the battles, the territorial disputes, and the never - ending family feuds. They believe that by running away, they can start anew and build a more harmonious existence for themselves.
One possible plot could be that they run away to escape the ongoing wizarding war. They find a secluded place, perhaps a hidden cottage in the Forbidden Forest. There, they start to understand each other better without the influence of their respective houses' prejudices. They might discover new magic together and form a bond that is deeper than friendship.
One possible plot could be that they run away to escape the chaos of the wizarding world. Maybe they are tired of the constant danger and politics. They find a secluded place, perhaps a hidden cottage in the Forbidden Forest. There, they start to build a new life together, learning magic in their own way, away from the prying eyes of Hogwarts and the Ministry. They might also discover new magical creatures and spells in their self - imposed exile.