Can the Green Card be Taken Away if the Foreign National Married Fraudulently?

Yes.

It may not be a common occurrence. USCIS does not make much of an effort to seek out fraud post-approval (it’s far more common for this to come to USCIS’ attention as part of the naturalization process), and proving fraud on the part of only one spouse after the fact tends to be difficult.

However, any fraud used in obtaining permanent residence can result in USCIS taking action to rescind permanent residence – which is why it is critically important to be truthful in all aspects of the application. USCIS may find out about any misrepresentation at any time, and legal action to rescind permanent residence is therefore always a possibility.