@IL-Tax-Pro "The state is mailing follow-up notices to the original taxpayers at their state income tax filing addresses. "

Why do you think they are doing that?  Maybe because they want to follow IRS instructions regarding this situation? I do expect both IRS and state agencies will be overwhelmed with fixing all the erroneous claims.  IRS can be incompetent sometimes, but it's easy enough for them to just shut off CP-2000 notices involving unemployment income, and in their best interest.  It's encouraging that at least Illinois is trying to prevent issuance of erroneous 1099-G forms. The sky is not falling.  Yet.  

From IRS on December 29:

If a payor or a law enforcement agency determines based on all facts and circumstances that, due to identity theft, payments made under an unemployment compensation program were not made to the individual under whose name the benefits were claimed, the payments should not be reported on Form 1099-G.

If payments made due to identity theft are mistakenly reported on Form 1099-G in the name of an identity theft victim, a corrected Form 1099-G reporting $0 should be issued to the identity theft victim and filed with the IRS as soon as possible after the error is discovered.

https://www.irs.gov/forms-pubs/identity-theft-guidance-regarding-unemployment-compensation-reporting