When a separation agreement is the basis for an award of spousal support, the court, in approving the agreement, shall examine the agreement to ascertain whether it clearly provides for spousal support to continue beyond the death of the payor or the payee or to cease in such event. When spousal support is to be paid pursuant to the terms of a separation agreement which does not state whether the payment of spousal support is to continue beyond the death of the payor or payee or is to cease, or when the parties have not entered into a separation agreement and spousal support is awarded, the court shall have the discretion to determine, as a part of its order, whether such payments of spousal support are to be continued beyond the death of the payor or payee or cease. In the event neither an agreement nor an order makes provision for the death of the payor or payee, spousal support other than rehabilitative spousal support or spousal support in gross shall cease on the death of the payor or payee. In the event neither an agreement nor an order makes provision for the death of the payor, rehabilitative spousal support continues beyond the payor's death, in the absence of evidence that the payor's estate is likely to be insufficient to meet other obligations or that other matters would make continuation after death inequitable. Rehabilitative spousal support ceases with the payee's death. In the event neither an agreement nor an order makes provision for the death of the payor or payee, spousal support in gross continues beyond the payor's or payee's death.