Can My Boyfriend Appeal If He Was Granted Voluntary Departure For Overstaying His Visa?

My boyfriend was locked up for overstaying his visa. At the hearing, he got “voluntary departure.” Can he appeal?
He could file a “Motion to Reopen or Reconsider” or a “Petition for Review”. Under the old rule, he would still be subject to the consequences of overstaying the voluntary departure period. Under the new rule for “voluntary departure” that went into effect on January 20, 2009, the filing automatically terminates the grant of voluntary departure. In both cases, the alternate order of removal takes effect.