Consult with an experienced immigration attorney who is going to need to get specific information from you and a more clear picture of the situation.
you may also want to make an info pass appointment at the USCIS and ask a officer. USCIS.gov
Your parents' immigration status will have no effect on your ability to stay in the U.S. Since you are a green card holder, the only way you will lose it is if you spend excessive time outside the U.S. or commit a crime that makes you deportable. Your parents may have issues coming back to the U.S., however. You may want to consider naturalizing and becoming a U.S. citizen.
www.gassonlaw.com - Disclaimer: This a general answer to your legal question. Unless you have a signed engagement letter with me, you should not consider this information to be legal advice.
I agree with attorney Mulder.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.