One of our cases currently pending at the Ninth Circuit raises the same issue, does the Board of Immigration Appeals lose jurisdiction to decide a Motion once the alien leaves the U.S.? The BIA has consistently held, yes, and the government has used this quirk in the regulations to quickly remove someone before the BIA rules on a pending motion.
For instance, our client was taken into ICE custody, we filed a motion to reopen along with an emergency motion for stay. The BIA denies the stay motion, never rules on the motion to reopen, and ICE puts our client on a plane back to his home country. The only recourse left to us was to file a petition for review with the circuit court. DOJ moved to dismiss the petition on the basis of no final order, as the motion to reopen was still pending, and the 9th Circuit issued an OSC. Our response was to invoke the BIA's "Post-Departure Bar Rule" as violating our client's procedural due process rights. Now the Sixth Circuit has agreed with our analysis of the BIA's rule.
"Pruidze’s petition for review raises one question: Does the Board of Immigration Appeals lack jurisdiction to consider an alien’s motion to reopen once the alien is no longer in the United States? The answer is no." Pruidze v. Holder, Feb. 3, 2011.