An employer can pay you any amount that he wants to for any reason that he wants to. However, an employer cannot just "at will" decide to classify payments as an expense advance, if the expenses have not been accounted for. If you have not documented actual expenses that were incurred in connection with your employment, then all or a portion of the $10,000 would be taxable income. The employer legally should include this amount in your taxable wages that are reported to you at the end of the year on your W-2 form, and you would be liable for taxes on this amount.
I would think as a starting point that you need to make an accounting of your actual out of pocket expenses to see if you really had enough to cover the $10,000 "expense advance" that you were given. You should then send an accounting of those expense to your employer to justify the amount you were given. If your actual expenses fall short of the $10,000, then at the very least you will be liable for taxes on the portion that was overpaid.
Aside from the tax issue, there is another issue with your employer now saying that they want the money back because the payment was not authorized. I guess the question is who authorized the payment to begin with? I would have to assume that was the employer. It seems to me that it would be very difficult if not impossible for them to come back to you now and demand repayment of this money, however, you should really seek the advice of an attorney in this field for an answer to that question. Just keep in mind that even if you do not end up having to repay this money, you may be liable for taxes on any portion that you cannot justify as actual expenses incurred.
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