This paper reconsiders necessary conditions for extinction of an animal population. Containing many of the models previously developed in the literature, the general model proposed here suggests that (i) conditions for extinction depend exclusively on the relation of a minimum viable population size to the minimum population size at which any exploitation is profitable, (ii) necessary conditions for extinction need not be characterized in terms of returns-to-scale parameters or growth rates as other authors have contended, and (iii) possible short-run shut-down may save a population from extinction if the fish population at the time of shutdown is large enough to sustain the species.