In the event, of one owner's death on a Joint with Rights of Survivorship account, the proceeds pass to the remaining owner. In the event of the death of both owners, the proceeds pass to any named beneficiaries. If no beneficiary is named, the beneficiary in most cases will be the estate of the last surviving owner. If you do want a specific person or entity to be paid in the event both owners have died, a beneficiary can be named.
* This scenario is in the context of non-qualified mutual funds, certificates, brokerage or SPS / Ameriprise ONE Financial Accounts when a 3214 TOD POD form is submitted. Review your contract details if you have questions about a jointly owned annuity product.