During the progression of cancer cells, the degree of genome instability increases leading to genome chaos in populations of malignant cells. While normally chaos is associated with er-godicity, i.e., the state when the time averages of relevant parameters is equal to their phase space averages, the situation with cancer propagation is more complex. Chromothripsis, a catastrophic massive genomic rearrangement, is observed in many types of cancer leading to increased mu-tation rates. We present an entropic model of genome chaos and ergodicity and experimental evidence that increasing the degree of chaos beyond the non-ergodic threshold may lead to the self-destruction of the tumor cells. We study time and population averages of chromothripsis frequency in cloned rhabdomyosarcoma from rat stem cells. Clones with frequency above 10% result in cell apoptosis possibly due to mutations in the BCL2 gene. Potentially this can be used for suppressing cancer cells by shifting them into a non-ergodic proliferation regime.