I beleive they were all already living in Salem. But there was a car accident, Billie came upon the scene. The dying mother asked Billie to look out for Chelsea, both parents died, Chelsea taken to hospital. When she needed blood, Billie proved a match, but did not know Chelsea was her daughter. Actually, Chelsea was already good friends with Abby, and was rather out of hand, sneaking out of the house, talking Abby into trying to dress older in order to get into Cheatin' Heart. Chelsea had a crush on Patrick, and was trying to sort of seduce him. LOL
After the parents died, Billie did take Chelsea under her wing to look out for her, as the parents were in debt, there was no insurance and the house was foreclosed, & Chelsea was left with nothing.