The type of cell that does not possess a true nucleus is called a prokaryotic cell.

Here's why:

* Prokaryotes are single-celled organisms that lack a membrane-bound nucleus and other membrane-bound organelles. Their genetic material (DNA) is located in a region called the nucleoid, which is not enclosed by a membrane.

* Eukaryotic cells, on the other hand, have a true nucleus that contains their DNA and is separated from the cytoplasm by a nuclear membrane.

Examples of prokaryotes include bacteria and archaea.