That seems to be Michigan law, at least according to Reardon v. Midland Community Schools (E.D. Mich. Sept. 2, 2011):
First, some brief attention needs to be given to Michigan law governing the obligation of parents to provide care and support to their children until the age of eighteen on the one hand, and yet, on the other hand, providing children the autonomous right to leave their parents’ home at the age of seventeen. See Mich. Comp. Laws §§ 712A.2(a)(2) & (3), 722.3, 722.151. Pursuant to Michigan Compiled Laws § 722.151, “[n]o person shall knowingly and wilfully [sic] aid or abet a child under the age of 17 years to violate an order of a juvenile court or knowingly and wilfully conceal or harbor juvenile runaways who have taken flight from the custody of the court, their parents or legal guardian.” Moreover, Michigan probate courts have jurisdiction to compel a juvenile who has deserted her home to return, at least until the juvenile reaches the age of seventeen. Mich. Comp. Laws § 712A.2(a)(2) & (3).
On the other hand, although Michigan law terminates the courts’ jurisdiction over runaway children at seventeen, it also provides that parents still have an obligation to support their children until they reach the age of eighteen. Under Michigan Compiled Laws § 722.3, “parents are jointly and severally obligated to support” their minor children, and Michigan courts may order parents to continue to support their children after they reach the age of majority. In Michigan, the age of majority is eighteen. Mich. Comp. Laws § 722.52. Absent an adoption, a biological parent’s obligation to support his or her children remains with the parent even if parental rights have been terminated. See Evink v. Evink, 542 N.W.2d 328, 329–30 (Mich. Ct. App. 1995). Whether these Michigan laws are well founded or not, they played a role in the events of this case.
I don’t know anything more about the subject, but I’d love to hear how this actually plays out in Michigan, and what other states have similar rules. Note also that it’s not clear from the opinion how the duty to support children interacts with the children’s right to leave home, but I assume that the legal duty is complied with if the parents offer the children room and board at the parental home; I take it that a child may not leave home and then demand, as a matter of law, that the parents pay for the child’s rent and groceries. This, though, is just my expectation — I don’t know exactly how Michigan law plays out in this respect.
UPDATE: A commenter points out that the 17-year-old girl in this case was “grant[ed] ... a guardian and conservator, as well as child support”; the parents appeal, and the case will be argued soon.