If the Illinois tax was withheld in 2021, your employer should make the correction in their payroll records and refund the mistakenly withheld Illinois tax to you. Then your 2021 W-2 will not show any Illinois income or Illinois tax withheld. In other words, they should make everything look like it should have in the first place, as if the error never occurred. The employer can get the mistakenly withheld tax back from Illinois. If the error was very recent, they might not actually have paid any of the tax to Illinois yet. They might not be happy about making the correction, but they can do it. And if it was their mistake, they certainly should correct it.
If any Illinois tax was withheld in 2020, it might be too late to correct it. In that case, you will have to file a 2020 Illinois nonresident tax return to get the tax refunded.
For either year, if your W-2 shows Illinois income and you file an Illinois nonresident tax return showing zero Illinois income, you can expect to get a notice from the Illinois Department of Revenue saying that your tax return is wrong and you have to pay the tax. You will have to reply to the notice with an explanation of the situation. If you file the Illinois tax return by mail, you can attach an explanation to the return, but they might ignore the attachment and send a notice anyway.
