In Matter of Montiel, the Board of Immigration Appeals (BIA) determined that in certain circumstances, administrative closure of a pending immigration court proceeding may be proper when a respondent is appealing his criminal conviction. The BIA found such action appropriate in Montiel's case, in part, because the conviction was what made him removable, and a reversal on appeal would mean that he was not removable as charged. Notably, the motion for administrative closure had been joined by the Department of Homeland Security. The BIA reiterated the case-by-case analysis required for a motion for administrative closure and reaffirmed the factors outlined in Matter of Avetisyan.
The full text of Matter of Montiel can be found here: http://www.justice.gov/eoir/vll/intdec/vol26/3834.pdf