We develop an overlapping generations model where consumption is the source of polluting emissions. Pollution stock accumulates with emissions but is partially assimilated by nature at each period. The assimilation capacity of nature is limited and vanishes beyond a critical level of pollution. We first show that multiple equilibria exist. More importantly, some exhibit irreversible pollution levels although an abatement activity is operative. Thus, the simple engagement of maintenance does not necessarily suffice to protect an economy against convergence toward a steady state having the properties of an ecological and economic poverty trap. In contrast with earlier related studies, the emergence of the environmental Kuznets curve is no longer the rule. Instead, we detect a sort of degenerated Environmental Kuznets Curve that corresponds to the equilibrium trajectory leading to the irreversible solution.