These living cells never enter into cell cycle.

Cells of the heart are permanently withdrawn from cell cycle and never undergo division even if a part of heart is damaged. But the epithelia cells are always in cell cycle and continuously new cells are formed to replace the lost cells. Liver cells if required can enter into cell cycle and starts dividing to replace the lost cells. Parenchyma cells, if suitable conditions are provided can enter into cell cycle and divide like as in tissue culture during callus formation.