An applicant must apply to the USCIS for Advance Parole in the event that he/she has an adjustment of status (green card) case pending while physically present in the United States, and wishes to travel abroad for emergency reasons. For example, take the case of a spouse of a US citizen who has already applied for a green card through the marriage. In this event, the spouse is not allowed to travel outside the US for any reason while the application is pending, except with special permission granted by the USCIS. This is known as "Advance Parole" If he/she travels abroad without this permission, the green card application will be terminated and the applicant will be denied permission to return to the US.
Advance Parole allows the applicant to travel abroad in the event of a family emergency, such as a death or serious illness of a family member abroad, and to return to the US without the fear of being denied re-entry.
However, Advance Parole does not guarantee re-entry to the US. It is best to apply for Advance Parole while the applicant is still in status, ie. the Visa used to originally enter the US has not yet expired. If the visa has already expired, the applicant runs the risk of being denied re-entry. In this case, it is better to be safe than sorry and wait until the actual green card has been issued before foreign travel is contemplated.
The application for Advance Parole is filed with the USCIS on Form I-131 along with supporting documents.