Not unless you're planning to lie to get it. If you did that again, with an overpayment fraud history, this time, they'd be likely to prosecute you.
Unemployment fraud, in which you repaid the overpayment is NOT a felony or a criminal charge upon your record, and it does NOT affect any decision regarding your eligibility for unemployment on a new claim. (You file a new claim every time the benefit year passes.) That old claim from ten years ago is long gone, as far as eligibility issues.
You say you paid back all the unemployment you had received fraudulently. If so, then there will be no effect upon your current claim, though the unemployment system can still go in and see that you had this overpayment and that it has been discharged.
They don't say, well, we'll take the employer's word on this one because this turkey lied to us ten years ago so she is liable to be lying again. Every new claim is a new case, and if there are issues, they are supposed to look at them with totally fresh eyes.
If you had NOT paid pack this overpayment, guess what? When you file your claim, and you are approved for benefits, if there is still money owed on that overpayment from ten, fifteen, howmanyever years ago, then they'll take the unemployment payments you receive on this claim until that old claim is fully paid off. Though your eligibility for a claim isn't affected, your weeks of benefit paments is taken to offset any money you owe back from a former claim. Once it is paid off, then you can begin actually receiving the benefits on the current claim. And there's no statute of limitations on such overpayments, they stay on your unemployment record forever even if they didn't prosecute you and you didn't pay them back.
The really serious consequence of filing another claim would happen if you tried, once again to cheat, lie and obtain benefits fraudulently. Even though you've repaid the old claim, that is still going to show. If the fraud unit gets hold of a new occasion where you have attempted to defraud the system, guess what? They are going to be a whole lot more likely to prosecute you criminally for this one. They sort of allow you one for stupid, especially if you pay the money back and cooperate with their investigation. But do it more than once, and you are very likely to be the one who goes to criminal court and gets plastered all over the news media.
So sure, file for benefits this time. Just be sure that you listen, ask questions, read the materials, think about what you are doing, clarify any issues you don't understand about receiving benefits, and DON'T LIE TO THEM, either about the conditions surrounding your termination or the weeks you worked or made a work search or refused a job or ANYTHING, and you'll be fine to draw benefits again.
