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Unfortunately, if your employer can prove that they truly did overpay you on your final check, they would typically be entitled to that money back. The reasoning is that the money as never yours to begin with, even if you had no reason to suspect you were overpaid and even if you used the money for other purposes. You have no entitlement to something that is not yours and so it must be returned.
The above noted, it would be a huge drain of your employer's resources to actually sue you to get this money back, so they have a large incentive to negotiate with you. In this circumstance, it would be entirely common to work out a payment plan and perhaps even a reduction to the principal amount you pay back. The precise arrangement is up to you and your employer to negotiate.
As for deductions and taxes are concerned, since you have not yet filed taxes for the year in which you received the overpayment, there is not much for you to do. Your employer will provide you with a W2 at the end of the year which accurately reflects your earnings. As far as what they paid on your behalf for taxes and with holdings, it is up to your employer to get that money back from the respective state and federal agencies. Those efforts really don't concern you as there is no adverse affect to you from your employer having paid more into the system on your behalf than they were supposed to.
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