According to Leonard Hayflick the cells have a right time to die, their lifespan is according to the size of the telomeres, if the telomeres become too short the cell dies. This telomere shortening limit is known as the Hayflick limit.
Hayflick noted that the cells divide approximately fifty times before they die. As the cells approached this limit, they showed more signs of old age. That is, according to Hayflick's limb, cells can divide only a certain number of times before they begin to age and stop reproducing, at which point the telomeres begin to shorten and the cell begins to senescence.
A. Hayflick limit