Payments that are in arrears do NOT terminate upon the death of the payee. It is money that should have been paid and was not. They become part of the payee's estate. The estate must clear probate before anything can be distributed to to beneficiaries. However, in this case, unless the beneficiary is the child the payments were paid to the mother for, an executor who is conscientious should treat that money separately and pay it to that child before dividing the remainder of estate assets equally according to the will. If the child in question is not named in the will, then while the money is technically part of the estate, the other beneficiaries are jerks if they object to the money going to the child.
However, all estate debt comes first, and if that means the child support money must go toward paying debt, so be it.
Child support payments that are NOT in arrears may be treated differently, and that can vary from state to state. In one state, current payments may terminate upon the death of the payee/custodial parent. If custody goes to the non-custodial parent who is making the payments, then of course the payments would stop. Every state can have its own rules on this.