It could also be that he is running away from his own past traumas. Sirius had a difficult family life with the Blacks. He might be running from the memories, the expectations of his family, and the dark magic associated with his family name. By running away, he is trying to find a new identity and a new start.
One possible reason could be to escape from false accusations. In the 'Harry Potter' universe, Sirius was wrongly accused of betraying the Potters. So in the fanfiction, he might run away to avoid being captured and to find a way to prove his innocence.
Well, perhaps they run away because they discover some dark secrets about the wizarding world that others don't want them to know. They might fear for their lives if they stay, so they choose to flee. It could also be that they are simply seeking adventure. The daughter of Harry and Sirius might inherit their adventurous spirits, and they both decide to run away to explore the unknown parts of the wizarding world and beyond.
One possible reason could be that she feels trapped in the strict rules and hierarchy of the academy. Maybe she discovers some dark secrets within the academy walls that make her fear for her safety or the safety of those she loves. Another reason might be a conflict with a powerful figure at the academy, like a teacher or an elder vampire.
Maybe he's tired of his restricted life. In the story, he might be feeling suffocated by all the rules and expectations placed on him, so he decides to run away to find freedom.
One possible reason could be family pressure. In the Weasley family, there are high expectations and a lot of chaos. Percy might feel suffocated and decide to run away to find his own path. Maybe he's tired of always being in the shadow of his more popular siblings and wants to prove himself on his own terms.
Another reason could be that Naruto is being targeted by a powerful enemy within Konoha. He doesn't want to put his friends and the village at risk, so he runs away to draw the enemy away from Konoha. This would show his selfless side, sacrificing his own safety for the greater good of the village.
It could also be due to a particularly bad encounter with someone in the village. For instance, if he was bullied severely by some older kids and he felt that there was no one to protect him. He might have thought that running away was his only option to avoid further harm.
Mal might run away in the fanfiction because she's constantly being judged for her past as a villain's daughter. Despite her efforts to fit in Auradon, there are still those who look at her with suspicion. She could also be running away from a future that she doesn't want. For example, if there are plans for her to take on a role she's not ready for or doesn't believe in, she may choose to escape.
The significance could be that it strengthens the bond between Sirius and the Potters. It shows that he trusts them completely.
One possible reason could be Naruto's internal conflict. In yaoi fanfiction, the relationship is often complex. Naruto might be running away because he's confused about his feelings for Sasuke. He may not be ready to face the intensity of the relationship that the yaoi concept implies.
Perhaps she is being chased by some unknown enemies in Konoha who are after her for some reason. She might think that running away from Konoha is the only way to protect herself and those she cares about. It could also be that she has a new mission or purpose that she believes can only be achieved outside of Konoha, and she is willing to sacrifice her life in the village for it.