If you have old child support arrears and someone dies and leaves you beneficiary, can the government take your inheritance

If the government knows about the delinquent outstanding CS, yes, the government can if it knows about the inheritance.

As noted, if they know about the inheritance before you received it, then certainly can seize it. Even after you receive it they can go after you, seize bank accounts etc.

Yes, but then of course a person should if they owed the money and get money, it would normally be paid?

So you are saying that you had or have old child support money you owe and just do not plan to ever pay it?