How long do we retain I-9s?

Q: “We are conducting a self-audit on our employees’ I-9s. Our understanding is that we only have to keep the I-9s for three years after their start date, or if they were here less than three years, we keep it for one year after they leave, whichever is longer. Is that correct? We are a government contractor. If we cannot find the E-Verify on a current employee, should we run them through even though they started far longer than three years ago?” – Donna, North Carolina