(a) If the sole executor or all the executors die, resign, or are removed, the probate court having jurisdiction of the estate must grant letters of administration, with will annexed, to the person entitled thereto under Section 43-2-27.
(b) If an administrator dies, resigns, or is removed, the probate court having jurisdiction of the estate must grant letters of administration of the goods and chattels, rights, and credits, unadministered, to the person entitled thereto, as in cases of intestacy.