The accumulation of senescent cells during aging contributes to the progression of various age-related pathologies. Ineffective immune clearance, increased half-life of senescent cells, and bystander senescence are considered the primary drivers of this age-associated accumulation. Most of these causes stem from the aging of the immune system, which results in a prolonged persistence of damaged/nonfunctional cells within tissues and allows the internal senescence program to progress to a more severe phenotype. Here, we propose the existence of an additional immune-independent mechanism underlying the accumulation of senescent cells during aging. By reanalyzing existing experimental evidence, we show that cells of diverse identities and tissue origins become increasingly susceptible to senescence with age. The latter implies that epigenetic and molecular changes that cells acquire during aging create a permissive background for the activation of the senescence program. In light of our findings, senotherapeutic interventions alone may be insufficient to substantially alter the trajectory of organismal aging. Effective strategies may need to target upstream drivers of cellular dysfunction, including age-associated epigenetic alterations. Epigenetic rejuvenation could, in principle, enhance cellular stress resilience and thereby reduce the rate at which senescent cells emerge and accumulate.