I don't think it's really said what was going on with his parents so far. Living with his older sister doesn't mean much in and of itself. A lot of Japanese high schoolers end up staying with a relative who lives closer to the school they got into, while their parents are still living somewhere else. Maybe the parent or parents are both overseas for work in those situations sometimes. So him living with his sister who seems to be working already doesn't automatically give us the answer, just a potential clue until they elaborate on it.