Yes, this definitely can happen because the 1099-C has been reported to the IRS. This document reports income from the forgiveness of debt, in your case your car loan. The IRS considers this to be taxable income.
The creditor can issue a 1099-C years after your repossession. The IRS says "a debt is deemed canceled on the date an identifiable event occurs or, if earlier, the date of the actual discharge if you choose to file Form 1099-C for the year of cancellation." See page 4 here: https://www.irs.gov/pub/irs-pdf/i1099ac.pdf for what is considered an "identifiable event."