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Medicare Answers
I've seen evidence indicating that underpayments can be paid to children upon the death of the original intended recipient.
From http://www.ssa.gov/oig/ADOBEPDF/audittxt/A-09-07-17119.htm :
Death underpayments occur when beneficiaries die before they receive all benefits due them or before they endorse a benefit check payable before the month of death. Death underpayments are payable to relatives or the legal representatives of the estates of deceased beneficiaries under the following order of priority established by the Social Security Act.
1. A spouse who was living with the beneficiary at the time of death or a spouse entitled on the same earnings record at the time of death.
2. A child entitled on the same earnings record.
3. A parent entitled on the same earnings record of the deceased person.
4. A spouse not entitled on the same earnings record.
5. A child not entitled on the same earnings record.
6. A parent not entitled on the same earnings record.
7. A legal representative of the estate.
See also http://www.ssa.gov/OP_Home/rulings/oasi/31/SSR70-03-oasi-31.html