Your friend has to file his 2019 tax return, and report the unemployment benefits that he received in 2019, as shown on his 2019 Form 1099-G. If he has to repay any of his 2019 unemployment benefits in 2020, that will be reflected on his 2020 tax return. If he has to repay in 2020 any unemployment benefits that he received in 2020, that will also be shown on his 2020 tax return.
The bottom line is that having his unemployment benefits audited in 2020 does not affect his 2019 tax return or stop him from filing his 2019 tax return. Any repayment of unemployment benefits is reported on the tax return for the year that he makes the repayment.
