My response:
Except as otherwise agreed to by the parties in writing, a spousal support order terminates upon the death of either party. [Fam C §4337] The exception permits the parties, by a property settlement agreement, to continue the obligation beyond the death of the supporting spouse and to make it enforceable against his or her estate. [Steele v Langmuir (1976, 2nd Dist) 65 Cal App 3d 459, 135 Cal Rptr 426] Thus, a marital settlement agreement provision requiring the husband to maintain life insurance for the wife, in an amount equal to the current value of his support obligation, was held to constitute a written agreement for the continuation of spousal support following the husband’s death. [Lucas v Elliott (1992, 1st Dist) 3 Cal App 4th 888, 4 Cal Rptr 2d 746]
However, because Spousal Support (SP) is set up in a Marital Settlement Agreement, and is therefore contractual in nature, arrearages of SP remain collectible from the Estate after death. Like any other debt that became chargeable prior to death, SP is likewise collectible as a debt against the Estate. But, again, SP orders terminate on death, and therefore, there's nothing more that your client can collect, other than what is currently owed.
Therefore, have your client file a creditor's claim against the Estate, immediately. As a matter of fact, have her see an Estate (Probate) attorney immediately, before the Estate is wasted.
Good luck.
IAAL