All organisms die, and most become more likely to die with age, a phenomenon called demographic senescence or ageing. Despite the previous sentence saying nothing about the particular shape of a mortality curve, most organisms age in remarkably similar ways. In particular, organisms across the tree of life experience exponentially increasing mortality hazards with age, a pattern called the Gompertz–Makeham law. In this talk, I will argue that senescence is an unavoidable consequence of the progressive accumulation of stochastic damage to, or failures of, intra-organismal subsystems (genes, cells, organs, etc) over time. In many organisms, ‘failure begets failure’ because sub-systems are interdependent. I will demonstrate that this interdependence generically produces Gompertz-Makeham mortality curves, and shows that more complex organisms should exhibit clearer ageing patterns. Since individuals who die can no longer age, observed cohorts become increasingly composed of ‘lucky’ individuals that avoided death by (stochastically) living lives associated with lower mortality, even if individuals have no intrinsic differences in quality at birth. Such "selective disappearance" of unlucky individuals generates deviations from Gompertz-Makeham predictions at advanced ages, producing a late-life mortality plateau. We show that while these deviations must always exist, they may often be difficult to detect because robust detection requires unreasonably large cohort sizes. Our work establishes Gompertz-Makeham curves arising from stochastic failure/damage accumulation as a null expectation in complex organisms with many interdependent sub-systems.