Your parents should immediately seek to consult with and hopefully retain a competent immigration attorney specializing in political asylum.
Please also note that obtaining permanent residency through asylum if truly qualified, is more advantageous than obtaining a green card through a USC son or daughter: with the grant of asylum come all kinds of government benefits and (medical, financial) which parents would not have otherwise been able to obtain or qualify for had they obtained their green card to their son's petition.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
I agree. You need a personal consultation. Your question is very case specific and requires review of the record. Details matter in these things. You also have 30 days to seek reconsideration which shall be done with an attorney on board.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
Whatever you decide to do, you'll want to move quickly. Schedule an appointment with an attorney (and you and your parents all need to go) to talk about the situation and if asylum is appropriate or if there's some other way to stay in the United States.
This general advice does not create an attorney-client relationship.