Doubt that is what happens, unless that billionaire is really stupid.

They already have their estate (money, properties, etc) in a trust fund. When the current beneficiary dies the trust has a secondary beneficiary listed. There is no inheritance tax, the next person in line just gets access (the benefits) to the trust. If that beneficiary dies, the next person on the list just gets the benefits of the trust.

Generally speaking who ever is the current beneficiary lists who gets it after them. Kind of like how we do a will.