If someone dies without a valid will, then this is described as an intestacy – they have died intestate. There are rules which govern what should happen to their estate.
A grant of probate is not possible as there is no will, but instead, power is invested in the applicant via a document called letters of administration. The Intestate Succession Act (ISA) details seven classes of people in descending order of priority who can apply to administer the intestacy. Because there is no will, there are strict rules about who will inherit.