If cancer cells have telomeres are they different than the telomeres in non-cancerous cells? Would cancer cell telomeres be somehow 'set-up' to function almost indefinitely; in other words are 'they' very 'robust' or 'durable'? If these cancer cell telomeres are 'durable could their functioning cause any apoptosis mechanisms to 'shut down'?
In a normal cell, during each replication the telomere is shortened slightly due to the end replication problem, as you probably know. As mutations occur and a normal cell begins to exhibit cancerous characteristics, it needs a way to stop the self-destruction which happens when the telomeres become too short. In fact it is the cancer cells themselves which 'short-circuit' the shortening process and cause the telomeres to stay long enough.
90% of tumors do this by activating telomerase, an enzyme complex which elongates telomeres and keeps them from getting too short, so that the cell is effectively immortal from this sort of destruction. Usually telomerase is not active in most cells, except for stem, germ, and hair follicle cells, but cancer cells use this to their advantage and activate it to stay immortal. The other 10% or so employ a method called ALT, or Alternative Telomere Lengthening, a not yet thoroughly understood process which involves the recombination of tandem repeats between sister chromatids.
This page explains how cancer cells bypass the telomere shortening process well, and also provides a series of further reading on telomeres and telomere shortening.
In cancer cells, the telomerase is not "formed" but activated, mainly due to an amplification and a gain of copy of the 5p chromosome arm, containing the gene coding for TERT. For example, a very common way to immortalize primary cells to establish a cell line is to stably express TERT.
Shortened telomeres initiates DNA damage response pathways, resulting in the activation of ATM and ATR, and downstream kinases CHK1 and CHK2, and phosphorylation of p53. Once activated, p53 upregulates genes that mediate cellular senescence and/or apoptosis.