This article about child support gives a great explanation:
If your former spouse is receiving Social Security Disability (SSD) benefits and is the payor of child support, it is important to know that your child is also eligible for certain benefits – known as SSD Dependency Benefits – and that they will have an effect on how much your former spouse must pay directly to you for child support.
Generally speaking, SSD benefits are meant to substitute for the lost earning power of a disabled worker. Put another way, the SSD benefits are intended to help compensate you for the pay you’re losing due to your disability and, therefore, your inability to work. If you are unable to work, and you have children, it stands to reason that you will need help supporting those children while you’re on disability. This is the purpose of the SSD Dependency benefits. While SSD payments belong to the disabled worker, SSD Dependency benefits belong to the child and are intended to help meet the child’s current needs.
In general, if the disabled worker is the parent paying child support, courts will credit SSD Dependency benefit payments against that parent’s child support obligation as long as the credit is being made against child support incurred contemporaneous with the benefit payment and if arrears exist. For example, let’s say the parent’s child support obligation for the period between April 2012 and August 2015 totaled $30,000, and the parent had only been able to pay $15,000 due to being out of work. If the child received a dependency benefit check for that same period in the amount of $20,000, then courts will allow for $15,000 of that $20,000 benefit to be applied to the arrears. Full article here: http://www.mondaq.com/unitedstates/x/414212/Family+Law/How+Do+Social+Security+Disability+Benefits+Affect+Child+Support