Employer didn't contribute FICA taxes
I work at a state college. When I was a student employee the college was not obligated to pay any FICA taxes. After I graduated I started working at the college as a full-time employee. Two years later the college admitted that there was a bug in their payroll system and that they had not been withholding any FICA taxes. They said I owed over $9000 to the government because of their mistake. They paid the taxes on my behalf and are now taking out money from each of my pay checks to reimburse themselves.
Obviously, if they had not had the bug in their payroll system I would have ended up paying this money over the two years I worked with them. However, am I obligated to pay my portion still? I've recently received a new job offer with another company. If I leave am I obligated to keep paying them back?
Any advice would be helpful,
Thanks!