You might want to bookmark this page:

https://www.irs.gov/newsroom/2020-unemployment-compensation-exclusion-faqs-topic-g-receiving-a-refun...

For instance: "We will send a notice when your account is corrected for the unemployment compensation exclusion. The notice will be mailed to the address we have on file for you. Usually, a notice of adjustment is received within 30 days of when the correction is made. Please keep this notice for your records."

Did your client get this notice?

"The client originally had a balance due but with the UCE adjustment has a refund."

But never paid? Because, yes, you are still supposed to pay. And no, they tell you not to also amend.