I have never heard of a requirement that states that interest must stop accruing on an IRA after the death of the IRA owner. However, once you have confirmed knowledge that the IRA owner is deceased, you must stop reporting any new activity under their SSN. Most often, a "dummy" account (or Beneficiary IRA) would be set-up for each named living beneficiary. The funding would be by transfer of the portion (percentage) of the IRA balance (including accrued interest) that they are entitled to, if there are multiple named beneficiaries. Some banks have a system that will automatically do this and others (like mine) have to be done manually.
Hope that helps.
Nothing changes, if nothing changes. (from a good friend of mine)