Demographers sometimes observe remaining lifespans in populations of individuals of unknown age, and such populations may have an age structure that is approximately stable. Our goal is to develop a method to estimate the age structure of a stable population with unknown ages by using the information about all deaths recorded in the population after first observation and until its extinction. In the particular case of stationary populations, it is known that there is a symmetry between the age composition and the distribution of remaining lifetimes. When trying to generalize this result to a less restrictive set-up of stable populations, such symmetry does not exist due to the population growth rate. Nonetheless, it is possible to establish a relationship between the number of individuals in a given age 'a', with the number of individuals with 'a' remaining lifetime until death, and an extra term that depends on that growth rate. This property may be especially relevant for the study of populations in which ages are unknown, but individuals are followed up until death. In population biology, for instance, one may think of a wild population that is captured at a certain time point, and then the deaths and the number of individuals that are still alive at each subsequent time point are recorded until extinction. That information can then be used to estimate the age composition at the time of capture, provided that the assumption of stability is not overly distorting and that it is possible to have an estimate of the population growth rate. In the case of human populations, historical records, that usually lack information about births but have more reliable data about deaths, are also a potential area of application.