Some cells have no Hayflick limit. Barring trauma from outside, they are immortal. They can be killed, but they do not age. But they do not age. Bacteria keep on dividing forever, until some outside agency kills them.
Cancer cells are similarly immortal.
They keep on dividing and dividing, endlessly, unless they are killed or their host dies. Inside the nucleus of virtually every cell in your body are the long strands or filaments called chromosomes. Human cells have forty-six chromosomes, except for the sex cells, which have half that number. DNA makes up the cell's genes. At the tip of each spindle-shaped chromosome is a sort of cap, called a telomere.