Once a juvenile turns 18 years old, LE will not force them to return them to their parents/guardians, or to state care. Some states will not force a even 17-year old to return to their home or go to state care. LE uses their judgement during the initial report as to how endangered the child is, and if the child is located, LE again uses their judgement Some situations have been so disturbing, that missing children cases are kept open even from past decades.
When very young children, and often pre-teen children are missing, LE responds quickly and with urgency. If there is evidence of impaired health and/or impaired mental state, LE responds quickly and with urgency for all ages. If there is evidence of an abduction, no matter what the age, LE will respond quickly and with urgency, and an Amber Alert if qualifications are met. If there is evidence of an adult predator that has lured the child/teen away, LE will respond with urgency, but sometimes not so quickly if the evidence of the predator can't be found immediately (just suspicions).
I am not qualified to say what happens if the child has been abducted by the non-custodial parent--there are too many different situations to provide one answer for LE response. I have seen that non-custodial parent abductions get an Amber Alert if LE determines that the child's life/health is at risk.
If the teen was just living in a self-chosen alternative, then once the teen reaches a certain age (for some states), or eighteen, they can go to LE and ask that their case be closed. This is the situation I believe you were referring to,
@madfrank.
I think the Arkansas code for missing persons, that
@mlhenn posted, contains the usual requirements for LE to consider when the missing child becomes legal age.
Edited for grammer.