Hi, My husband is in the same situation as your boyfriend.
The first thing he needs to do is go the child support office that handles his case (which county did the divorce occur) and get a copy of his file. He needs to make sure everything is exactly correct.
In order for the State to be reimbursed, the State keeps child support payments if a person is receiving welfare (food stamps don't count as welfare). Any portion above the monthly welfare amount that the welfare recipient received (his ex) is given to the ex. There is a minimum amount the state is required to give the ex, I believe it is $25 or $32 for some reason, please check on that. So, the ex was getting at least, say, $25/month support. Make sure this was deducted from his amount owed.
It can be a very tiring task getting records and scouring through them, but you do not need an appointment to request your records, simply walk in to the local office that handles his case. He should call the 800 number to find out which office or he may already know. It is well worth the time! He does not need to ask the ex for an agreed pay off amount. His caseworker will handle that, once he tells the caseworker how much he wants to offer as pay off. Tell him to be reasonable. The bottom line is, he owes it. However, make sure he confirms that the amount they say he owes is correct. Maybe a payment slipped by, etc. It happens, but really, the child support division is pretty much accurate.
If the ex does not agree to a pay off amount (that is if the money is actually hers and not the state's), then he should get a loan and pay off the entire amount ASAP. Payments on a loan will definitely be less than his monthly child support payments. If a loan is not possible, try to get a high-limit credit card and pay off. If he only has a credit card with, say, $2000 limit, then he needs to get as many as he can. Perhaps he can sell his vehicle and use that money to pay off and then finance another vehicle once the pay off has gone through (it will look good on his credit).
We are in the process of taking cash out on a credit card and paying off the child support. Fortunately, my husband's ex agreed to about half of what is actually owed, because the other half is interest,and she is kind enough not to care about receiving the interest.
Yes, it seems unfair, but arrears are arrears and must be paid.
Email me if you have questions.