You should discuss it with your employer asap.
If you dont tell them,
case 1, nothing happen, they don't care.
case 2, if they find it later and they are serious. They will give the debt to a collection agency. It will injure your credit score for 7 yrs and you can't dispute such debt (unless you dont care your credit). And like you said, it's 6000 dollars matter, they will take you to the small claim court.