The likely thrust of any action against your husband will be administrative collection efforts by the state to recover any UC benefits overpaid to him. I have had no experience where the state or county criminally prosecuted for recovery of benefits, but my understanding from my partner (who has prosecuting and defending criminal claims for nearly 30 years) is that there is little one can do proactively to fend off commendatory of criminal prosecution. If and when a criminal action is brought against you or your husband, seek legal representation.
Consult with a criminal defense attorney about the situation. It is unlikely that this will be ignored forever. Experienced counsel can advise you on any benefit in being proactive about the situation.
This answer does not create an attorney-client relationship. It is advisable to consult with an attorney with full disclosure of relevant facts for a comprehensive leagl opinion.
I'd recommend you and your husband consult with an employee-rights attorney licensed in MN. You can search for such an attorney at www.nela.org.
Most MN attorneys you find at that website will be familiar with MN unemployment law, and the State's procedures in handling unemployment "fraud" allegations, including whether that State gets its criminal authorities involved or if a criminal conviction could result from unemployment issues.
In my State of Wisconsin, I have encountered workers ACCUSED of unemployment fraud or omission (whether they are FOUND to have unemployment fraud is a matter to be determined after a hearing conducted by the WI unemployment agency), but in those situations the potential penalties were not criminal, and rather were part of the unemployment agency's proceedings.
An MN-licensed employee rights attorney you find via nela.org should be able to give you sound advice for the unemployment proceedings, and should also know whether MN's unemployment agency involves any sort of criminal authorities in their unemployment fraud proceedings. If at any point you are told there is a criminal authority or allegation involved, you should consult with an MN-licensed criminal defense attorney.
The answer above is not legal advice. You can contact me directly at email@example.com. My web bio is here: http://www.pbclaw.com/our-people/attorneys/michael-brown/. For legal advice, you will need to consult directly with an attorney about the details of your situation.