Well, in some 'the girl with the vampire family fanfiction', the girl might be a vampire hunter who, for some reason, ends up living with a vampire family instead of killing them. This creates a very tense and interesting dynamic. She could gradually come to understand that not all vampires are bad and form deep bonds with them. There could also be a story where the girl is a psychic and is able to communicate with the vampires in a way that no one else can, leading to her becoming an important part of their family.
There are many 'the girl with the vampire family fanfiction' out there. Some might involve a girl who falls in love with a member of the vampire family. This could lead to all sorts of drama, like trying to keep the relationship a secret from the rest of the family or dealing with the fact that she's mortal and he's not. Others might be more about the girl's role in helping the vampire family face a threat, perhaps from other supernatural beings.