There are a few cell types that remain in a non-dividing stage and do not complete the mitosis process. These cells are often referred to as being in G0 phase, a quiescent state outside the normal cell cycle.

Here are some examples:

* Neurons: Once mature, neurons typically do not divide. They are highly specialized cells that are essential for brain function, and their loss is difficult to repair.

* Cardiac muscle cells: Similar to neurons, cardiac muscle cells have a limited capacity for regeneration. They mostly stay in G0 phase after reaching maturity.

* Skeletal muscle cells: While some skeletal muscle cells can divide, most remain in G0 phase after development. They can enlarge, but new muscle fibers are typically formed by the fusion of satellite cells.

* Red blood cells: After losing their nucleus and other organelles during maturation, red blood cells are unable to divide. Their lifespan is relatively short, and they are constantly replaced by new cells produced in the bone marrow.

It's important to note that while these cells generally do not divide, some factors can influence their ability to enter the cell cycle again, such as injury or specific signaling molecules. However, their primary state is one of non-division.