We report an intrinsically precise relation of the barium-to-iron enrichment as a function of age for a local, volume-complete (N = 30) sample of ancient Population II (tau >= 12 Gyr) and intermediate-disc stars (tau similar or equal to 10 Gyr), which suggests a common, r-process-dominated nucleosynthesis site for both elements in the early stages of the Milky Way. Deviants from this empirical relation are to a large extent identified as formerly known or new blue straggler stars. We report in particular the striking case of the Population II star HD159062, whose barium overabundance is difficult to explain without wind accretion of s-process material from a former asymptotic giant branch (AGB) primary that very likely survived as a white dwarf companion. The weak but significant barium enhancement that we measure for HR3578 and 104 Tau also suggests that both may be accompanied by faint degenerate companions. If confirmed through precision astrometry or direct imaging observations, this would mean a very efficient method to uncover ancient stellar remnant companions around solar-type stars.