Government accounting errors

I was wondering about the ability of the government, primarily state governments to recoup monies given as over payments to beneficiaries.

What I mean by beneficiaries are any accounts payable, whether it be a welfare recipient or a payment to a contractor, etc. You see, I personally have seen how the state government plays a lot of monetary games through its arm called the department of health and human services. What they do is a running game of changing the amount of benefits payable to a recipient based on criteria and sometimes, sometimes they reduce current payments using past over payments as the excuse for shortening what someone might receive.

All this is fair to balance an account ledger, however if someone makes an error of a payment, shouldn't the beneficiary be eligible to fight it in a court because the payer is negligent?

I know this sounds like just squabbling but if someone over pays you for something, is it a right to recoup monies just because you find the error later? The government seems to have the ability to do this all the time, but I can't see how a normal person can make these type mistakes and make a case for it in a court of law.