Eventually the cells die. The exception is stem cells, which use telomerase to rebuild their telomeres, allowing them to retain their ability to divide, and to develop ("differentiate") into virtually any cell type for the specific tissue or organ, be it skin, heart, liver or muscle--a quality known as pluripotency. These qualities make stem cells promising tools for regenerative therapies to combat age-related cellular damage and disease.
"In our experiments, limiting telomere length compromised pluripotency, and even resulted in stem cell death," says Teresa Rivera, a Salk research associate and first author of the paper. "So then we wanted to know if increasing telomere length increased pluripotent capacity. Surprisingly, we found that over-elongated telomeres are more fragile and accumulate DNA damage."
If we were somehow able to create "very long telomeres" in humans, then this would be something to worry about! We still have the length in children/teenagers, when health is close to optimum and cancer incidence is low.