At the age of 16, a young person can walk out of their parent's home and never have anything to do with them again. (If their parents reported the person missing, and the police located that person, the police would not be allowed to reveal their location to their parents). So it follows that the young person could, if he/she chose, go to live with another family member at the age of 16.
Prior to the age of 16, a young person normally requires their parent's permission to move out. However, it's not particularly unusual for younger teenagers to live with other adult family members. (Social Services, for example, don't normally get involved in informal 'fostering' arrangements, within the family, unless there are specific areas of concern)
Chris
(PS: That applies to the UK - or at least to England & Wales. Different rules will apply elsewhere)