If the employer was supposed to withhold $10,000 of social security and medicare taxes, that means they were supposed to send $20,000 to the government (they match your withholding). If they file amended tax returns to report and pay that $20,000, there are IRS regulations that allow them to recoup the $10,000 from you. If the employer doesn't recoup the $10,000 from you, they must report it as taxable income on your W-2 (possibly all in 2024, possibly by issuing corrected W-2s for all the past years).
There could be a law in your state that prevents employers from taking your money to fix this kind of mistake. You would have to contact your state labor department. But if they don't recoup the taxes, the money is extra taxable income for you.
