Such cells use environmental signals to coordinate growth with division. Differentiated cells are not fully occupied with S phase and M phase and spend most of their time prior to commitment to S phase, in G1, or prior to commitment to M phase, in G2. In G1, a liver cell can be a liver cell and brain cell be a brain cell. In G2, unfertilized oocytes remain in stand-by mode for decades. There are, obviously, many examples of terminally differentiated cells that undergo few or no cell divisions.
Neurons are good examples of how there can be growth without division.
Typically, growth factors are required to commit cells to S phase. Oncogenic mutations and losses of tumor suppressor genes frequently override growth factor requirements and other cell division controls. The yeast, Saccharomyces cerevisiae , is a single-celled fungus which exercises developmental options at the G1 stage of its cell division cycle. Starvation of yeast for nutrients arrests them as small, unbudded cells in early G1 phase. Addition of nutrients to early G1-arrested cells allows them to begin growing.