Adaptive response to stress is a fundamental property of living systems. At the cellular level, many different types of stress elicit an essentially limited repertoire of adaptive responses. Epigenetic changes are the main mechanism for medium- to long-term adaptation to accumulated (intense, long-term, or repeated) stress. We propose the adaptive deregulation of the epigenome in response to stress (ADERS) hypothesis which assumes that the unspecific adaptive stress response grows stronger with the increasing stress level, epigenetically activating response gene clusters while progressively deregulating other cellular processes. The balance between the unspecific adaptive response and the general epigenetic deregulation is critical because a strong response can lead to pathology, particularly to malignant transformation. The main idea of our hypothesis is the continuum traversed by a cell subjected to accumulated stress, which lies between an unspecific adaptive response and pathological deregulation—the two extremes sharing the same underlying cause, which is a manifestation of a unified epigenetically mediated adaptive response to stress. The evolutionary potential of epigenetic regulation in multigenerational adaptation is speculatively discussed in the light of neo-Lamarckism. Finally, an approach to testing the proposed hypothesis is presented, relying on either the publicly available datasets or on conducting new experiments.