No. That (moving out) alone will not disqualify the student from being a DEPENDENT. It will only disqualify him from being a Qualifying Child (QC). He can still be a Qualifying Relative (QR) dependent.
Mom will lose the EIC when the student goes from being a Qualifying Child to Qualifying Relative. Or, at least the child related portion of the EIC. Or more specifically the portion related to that particular child. So, yes, it's an over simplification to say Mom will lose the EIC. She may have other qualifying children and/or income low enough to qualify on her own. It's safe to say her EIC will be reduced and most likely, significantly.
Once again, we don't have all the facts. I assumed the student was going to school locally. Carl is correct, if he is living away from home for the primary purpose of attending an out of town school, he is considered to still be living with the parent and can be a QC
