Excessive exploitation diminishes the capacity of natural resources to withstand environmental stress, increasing their vulnerability to extreme conditions that may trigger abrupt changes. The onset of such events depends on the coincidence of random environmental conditions and the resource state (determining its resilience). Examples include species extinction, ecosystem collapse, disease outburst and climate change induced calamities. The policy response to the catastrophic threat is measured in terms of its effect on the long-term behavior of the resource state. To that end, the L-methodology, developed originally to study autonomous systems, is extended to non-autonomous problems involving catastrophic threats.