The asymmetric molecular emission lines from dense cores reveal slow, inward motion in the clouds’ outer regions. This motion is present both before and after the formation of a central star. Motivated by these observations, we revisit the classic problem of steady, spherical accretion of gas on to a gravitating point mass, but now include self-gravity of the gas and impose a finite, subsonic velocity as the outer boundary condition. We find that the accretion rate on to the protostar is lower than values obtained for isolated, collapsing clouds, by a factor that is the Mach number of the outer flow. Moreover, the region of infall surrounding the protostar spreads out more slowly, at a speed close to the subsonic, incoming velocity. Our calculation, while highly idealized, provides insight into two long-standing problems – the surprisingly low accretion luminosities of even the most deeply embedded stellar sources, and the failure so far to detect spatially extended, supersonic infall within their parent dense cores. Indeed, the observed subsonic contraction in the outer regions of dense cores following star formation appears to rule out a purely hydrodynamic origin for these clouds.