The way I read the original question was that the deceased had not yet been paid the the underpayment due the deceased based on the deceased's entitlement to SSDI benefits. The guy died before his benefits could be paid to HIM (or her, as the case may be). The spouse who lived with the deceased at the time of the deceased's death is the first person who is eligible to be paid the underpayment due the deceased for SSDI.

In re-reading the question, I now realize that the question may not have meant what I originally thought. Was the original poster referring to the underpayment due the deceased, or ongoing survivor benefits?

My answer had nothing to do with receipt of survivor benefits. A father's obligation to pay child support does not then become the responsibility of the child who receives survivor benefits. The father's debt will not be garnished from the child.