An elementary, probabilistic model for fiber failure, developed by Coleman in the fifties of the last century, predicts a Weibull distributed time-to-failure for fibers subject to a constant load. This has been experimentally confirmed, not only for fibers but for load-bearing products in general. In this paper, we analyze residual strength, i.e., the strength after having survived a given load program. We demonstrate that the Weibull modulus, describing variability of time-to-failure, affects residual strength. It determines (a) how fast residual strength of fibers decays during their service life, (b) the residual strength variability, and (c) the fraction of surviving fibers during service life. Experiments show that residual strength of Twaron fiber (p-aramid fiber), exceeding predictions of Coleman's model, remains unrelentingly high (close to virgin strength) during service life.