What product is out there for an elder who wants one of her siblings to take care of money matters when incapacitated or dead?

Actually a Power of Attorney allows someone to represent another person. Once the person died, there is no longer someone to represent.

I still take care of my Dad's financial matters even though he has passed and I was his financial Power of Attorney. I am my Dad's Executorix in his Will, thus the job continues until said financials officially passed over to me.

Therefore, if the elder whats her sibling to continue handling the financials, then the elder should make mention of that in the Will or make her sibling Executor.

A Durable or springing Power of Attorney can address handling financial matters when someone is incapacitated. A Will or Trust is used for handling financial issues after someone's death.