There is a special rule that allows you to forgo claiming the student as a dependent and the student is then allowed to claim the NON refundable portion of the AOTC or the LLC (the TFD has not been renewed for 2018). But since they are non refundable, the student would have to have a tax liability for that to be of any benefit. You would lose the $500 dependent credit. They still can't claim themselves, but with the elimination of the personal exemption and the higher standard deduction ($12K single*) , that's not as important as it used to be.
*the standard deduction for someone who can't claim himself is limited to the lesser of $12K or his earned income + $350
