I agree. You and the in-laws are confused about what the letter means. Your in-law paid into the unemployment insurance system and now his former employee is drawing against that insurance. It might have resulted in higher unemployment taxes for your in-law had he kept the business going, but since he did not, it won't effect him.
However, he needs to do whatever his state requires to officially shut down his business and shut down his payroll account and unemployment accounts with the state.

