The foreign national may be granted this benefit at the conclusion of removal proceedings if the foreign national has been physically present in the United States for at least one year prior to receiving the Notice to Appear (the document that indicates that they are in removal proceedings), has been a person of good moral character for at least five years prior to being placed in removal proceedings, is not deportable for any of the criminal grounds of removal, and can establish that it is their intention to depart the United States. 

The Immigration Judge has the discretion to grant a period of at least 120 days for the foreign national to depart.  Many attendant circumstances and potential consequences follow a grant of voluntary departure and should be discussed with an attorney in greater detail.