It should be. However you should check with a local family law attorney.
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Law Office of Luis A. Guerra (954) 434-5800. This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice.
The fact that the woman was undocumented does not make the marriage illegal. Neither does tha fact that she purchased a fake social security card. There could be other reasons that the marriage would not be valid, such as she may still be married to a prior husband.
The marriage is still valid. For marriage purposes it is irrelevant what an individual's immigration status is or whether or not their social security card is valid. Remember, the social security card is a document that ,while often used for identification, is meant for the social security administration. That has nothing to do with marriage.
Your relative and his wife should see an immigration attorney to see if their is an option for her to adjust her immigration status and then obtain a valid social security card.
Andre Olivie, Esq.
Legal disclaimer: This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Do not rely on this advice without speaking to an immigration attorney in detail about your case. This message does not create an attorney-client relationship.