Sometimes, a cell does not stop dividing once it reaches the Hayflick Limit. This generally means that the telomeres are lost, and as a result, the overall integrity of the chromosomes are in a state of decline with each cell division.

Exposed chromosome ends are normally fixed by sticking the ends back together. The cell does this normally, but in this case sticks together the ends of different chromosomes. Certainly this temporaraly solves the problem of no telomeres. However, the fused chromosomes are randomly ripped appart which goes on to cause many mutations.

As this process continues, the cell becomes very unstable and reaches a critical point where it must either undergo programmed cell death (apoptosis), or because of one of the random mutations, telomerase has to be turned back on. (The genes for telomerase are present in every cell in the body, they are just silenced in most). If this occurs, telomerase become active, the telomeres are rebuilt and the cell becomes stable.

Cells that have been severely mutated and have active telomerase could very well become cancerous cells. Cancer cells are considered 'immortal' because telomerase activity allows them to divide forever, which is why they can form a tumor.

Cancer is difficult to fight because the immune system cannot recognize it, and furthermore, cancer cells are immortal. Essentially they will always continue dividing.

Because telomerase is necessary for the immortality of 80% of all cancer types, it is currently thought to be a potential drug target. If a drug can turn off telomerase in cancer cells, the above process will repeat itself: telomeres will be lost as the cells continute to divide, mutations will occur and cell stability will decrease. However, the cells would only have one option when they arrive at the critical point, they must die, because the drug would block telomerase activity.