Oxidative stress, perturbations in the cellular thiol level and redox balance, affects many cellular functions, including signaling pathways. This, in turn, may cause the induction of autophagy or apoptosis. The NRF2/KEAP1 signaling pathway is the main pathway responsible for cell defense against oxidative stress and maintaining the cellular redox balance at physiological levels. The relation between NRF2/KEAP1 signaling and regulation of apoptosis and autophagy is not well understood. In this hypothesis article we discuss how KEAP1 protein and its direct interactants (such as PGAM5, prothymosin α, FAC1 (BPTF), and p62) provide a molecular foundation for a possible cross-talk between NRF2/KEAP1, apoptosis, and autophagy pathways. We present a hypothesis for how NRF2/KEAP1 may interfere with the cellular apoptosis-regulatory machinery through activation of the ASK1 kinase by a KEAP1 binding partner—PGAM5. Based on very recent experimental evidence, new hypotheses for a cross-talk between NF-κB and the NRF2/KEAP1 pathway in the context of autophagy-related “molecular hub” protein p62 are also presented. The roles of KEAP1 molecular binding partners in apoptosis regulation during carcinogenesis and in neurodegenerative diseases are also discussed.