In the lifecycle of microorganisms, prolonged starvation is prevalent and sustaining life during starvation periods is a vital task. In the literature, it is commonly assumed that survival kinetics of starving microbes follows exponential decay. This assumption, however, has not been rigorously tested. Currently, it is not clear under what circumstances this assumption is true. Also, it is not known when such survival kinetics deviates from exponential decay and if it deviates, what underlying mechanisms for the deviation are. Here, to address these issues, we quantitatively characterized dynamics of survival and death of starving E. coli cells. The results show that the assumption--starving cells die exponentially--is true only at high cell density. At low density, starving cells persevere for extended periods of time, before dying rapidly exponentially. Detailed analyses show intriguing quantitative characteristics of the density-dependent and biphasic survival kinetics, including that the period of the perseverance is inversely proportional to cell density. These characteristics further lead us to identification of key underlying processes relevant for the perseverance of starving cells. Then, using mathematical modeling, we show how these processes contribute to the density-dependent and biphasic survival kinetics observed. Importantly, our model reveals a thrifty strategy employed by bacteria, by which upon sensing impending depletion of a substrate, the limiting substrate is conserved and utilized later during starvation to delay cell death. These findings advance quantitative understanding of survival of microbes in oligotrophic environments and facilitate quantitative analysis and prediction of microbial dynamics in nature. Furthermore, they prompt revision of previous models used to analyze and predict population dynamics of microbes.