You said the person "has never paid NYC income taxes on their paychecks." Are you looking at tax withheld from their paycheck, or at the New York City tax on their tax return? Even if they somehow managed to not have any New York City tax withheld from their pay, they might still be paying New York City tax on their tax return. New York City tax is included on the New York State tax return. It is not a separate tax return. If the person has always worked in a neighboring state, such as New Jersey or Connecticut, the out-of-state employer might not withhold New York City tax.
That is only one possible explanation. As macuser_22 said, no one can give you a definite answer to your question without knowing the person's circumstances and being able to see their tax return.
