An immigrant is always free to leave the United States voluntarily prior to the beginning of removal proceedings.  Following conviction or admission of an offense that triggers inadmissibility (e.g., a crime involving moral turpitude), however, a noncitizen will likely be deemed inadmissible if s/he tries thereafter to re-enter the United States.

 

            At the border, a noncitizen may be granted voluntary departure or allowed officially to withdraw an application for admission, or may be informally turned back.  See N. Tooby & J. Rollin, Criminal Defense of Immigrants § 15.16 (4th Ed. 2007).

Ninth Circuit

RELIEF - PRE-HEARING VOLUNTARY DEPARTURE
United States v. Becerril-Lopez, 541 F.3d 881 (9th Cir. Aug. 29, 2008) (immigration judge was not required to give advice of availability of pre-hearing voluntary departure, under pre-IIRAIRA law, because the relief would have been granted prior to the respondents appearance before the IJ). Note: The court gave no opinion on the possible outcome of this issue had post-IIRAIRA rules applied, which allow the IJ to grant "pre-hearing" voluntary departure at the master calendar hearing. INA 240B(a)(1).

Tenth Circuit

RELIEF " NON-LPR CANCELLATION OF REMOVAL " CONTINUOUS PHYSICAL PRESENCE REQUIREMENT
Barrera-Quintero v. Holder, 699 F.3d 1239 (10th Cir. Nov. 15, 2012) (voluntary departure under threat of deportation breaks physical presence for purposes of non-LPR cancellation of removal).