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Thank you for your question.
I'm afraid I don't have good news for you. A private agreement to modify child support that was not made a court order is not binding on the court. The court does not have to uphold the agreement, and it is possible that his ex-wife can now go back to court and recoup the amount owed. If she takes him back to court, your husband can (and should) try to defend by saying that they had an agreement for a lesser amount, and show evidence that he lost his job at the time the agreement was made. If he suspects that she will try to go back to court and recoup that money, it may be wise to file a motion to modify the child support at this point to at least have future payments reduced.
The support order will consider his average income over the last month or so. Usually the arrearage ordered to be paid each month is a percentage of the current support amount (such as 20%). It is usually low so as to allow the parent to be able to keep current on support amounts.