The evolution of established cancers is driven by selection of cells with enhanced fitness. Subclonal mutations in numerous epigenetic regulator genes are common across cancer types, yet their functional impact has been unclear. Here, we show that disruption of the epigenetic regulatory network increases the tolerance of cancer cells to unfavorable environments experienced within growing tumors by promoting the emergence of stress-resistant subpopulations. Disruption of epigenetic control does not promote selection of genetically defined subclones or favor a phenotypic switch in response to environmental changes. Instead, it prevents cells from mounting an efficient stress response via modulation of global transcriptional activity. This "transcriptional numbness" lowers the probability of cell death at early stages, increasing the chance of long-term adaptation at the population level. Our findings provide a mechanistic explanation for the widespread selection of subclonal epigenetic-related mutations in cancer and uncover phenotypic inertia as a cellular trait that drives subclone expansion.