The U.S. Citizenship and Immigration Services (USCIS) recently published a fact sheet regarding traveling outside the United States for asylum applicants, asylees and lawful permanent residents who obtained that status based on asylum status.
1) Asylum applicants: Asylum applicants who leave the U.S. without first obtaining advance parole via Form I-131 will be presumed by USCIS to have abandoned their asylum application. Please not that advance parole will not guarantee that the applicant will be able to return to the U.S. The applicant will still be required to undergo inspection by a USCIS immigration inspector.
2) Asylees: Asylees, those that have been granted asylum in the U.S., can travel abroad after receiving approval from the Secretary of the Department of Homeland Security via a refugee travel document. These documents are valid for one-year periods and are issued to asylees so that they may return to the U.S. after temporarily traveling abroad. It is suggested by USCIS that asylees obtain the refugee travel document before leaving the U.S.; however, in certain cases, this document may be issued abroad. Again, please note that the refugee travel document does not assure re-entry into the U.S. Asylees will also be required to undergo inspection by a USCIS immigration inspector.
3) Lawful Permanent Residents: Lawful permanent residents who obtained their immigration status based on their asylum status are allowed to travel abroad with refugee travel documents. Please see the above description (Asylee) for more information about international travel.
PLEASE NOTE: Asylum applicants who leave the U.S. without advance parole and return to the nation where they claimed to have been persecuted will be presumed by USCIS to have abandoned their asylum application, unless the applicant has a viable reason for that return visit.