Years ago I had a wife who never reported her income from DC, even though she had lived in CA her whole life and had never worked. This was back in the 80's and it took almost an act of Congress to get SS to issue her a new card with a new number. Probably the card she had, and that I used on the tax return was issued to her just based on name. 

My favorite is 078-05-1120 https://www.ssa.gov/history/ssn/misused.html