Section 16. Every person committed to the department until the age of eighteen as a delinquent child, if not already discharged, shall be discharged when he reaches his eighteenth birthday, unless a petition is filed by the department under section seventeen. Every person committed to the department until the age of nineteen as a delinquent child, if not already discharged, shall be discharged when he reaches his nineteenth birthday, unless a petition is filed by the department under section seventeen. Every person committed to the department until the age of twenty-one as a delinquent child or youthful offender, if not already discharged, shall be discharged when such person reaches his twenty-first birthday. The department may continue to have responsibility for any person provided for in this chapter under twenty-one years of age for the purposes of specific educational or rehabilitative programs, under conditions agreed upon by both the department and such persons terminable by either.