If a human did not age then they would not expire.

The process of ageing generates a gradual decay in the DNA contained within cells. When cells divide the process is not perfect and a few base pairs are lost from the end of chromosomes. This is usually not a problem as the ends are protected by long regions of "junk DNA" known as telomeres. These telomeres seem to have no function other than to protect coding regions of the genome.

When the telomeres have been degraded over several decades then any loss of DNA in each cell division may begin to impair gene function. This is the process of ageing.

In theory if ageing did not occur and the individual did not succumb to disease or injury, they could be considered immortal.

In cancer cells the enzyme telomerase becomes active to allow the cancer cells to divide indefinatly.

Hope this helps your quest for immortality