The lack of mass drift observed in Kr-induced collisions is explained assuming energy and particle transfer from the light to the heavy fragment during the equilibration stage in asymmetric heavy-ion reactions. Transferred energy and particle number can be estimated from the interfragment thermal equilibrium distribution provided the initial partition is known which we calculate within a semiclassical theory based on TDHF. The experimental findings are consistent with the theoretical predictions. In particular, the experimental mass drift as function of total kinetic energy loss is quantitatively described within a modified diffusion model which takes into account the mass exchange prior to the transport stage.