You should contact an immigration attorney to review the convictions to check whether it's for a crime involving moral turpitude or an aggravated felony. Since they are here illegaly, also it's important to evaluate if there's any immigration relief for which they qualify.
A foreign national who has been convicted of a felony could face serious immigration consequences, including removal from the US. It is crucial that you get the help of a qualified immigration attorney.
I agree with my colleagues. The question becomes whether the conviction constitutes an aggravated felony or merely a crime involving moral turpitude (CIMT). One CIMT conviction will not subject them deportation on criminal related grounds so long as it occurred more than 5 years after their admission. And aggravated felony conviction dooms them. That said, since they are undocumented they may be taken into custody, and immigration court proceedings will be instituted for their other immigration law violations. the question then becomes if they are subject to the mandatory detention provisions of the law.
Bottom line, they need good representation now.
It's not a matter of "if" they get your parents, it is a matter of when. Contact an immigration attorney ASAP as they may be able to advise your family and get them released on a bond ASAP. My firm handles deportation defense.
Law Offices of Nicklaus Misiti
212 537 4407
Legal disclaimer: The statement above is general in nature, 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.