We find that applying a theoretical wind mass-loss rate from Monte Carlo radiative transfer models for hydrogen-deficient stars results in significantly more leftover hydrogen following stable mass transfer through Roche-lobe overflow than when we use an extrapolation of an empirical fit for Galactic Wolf-Rayet stars, for which a negligible amount of hydrogen remains in a large set of binary stellar evolution computations. These findings have implications for modelling progenitors of Type Ib and Type IIb supernovae. Most importantly, our study stresses the sensitivity of the stellar evolution models to the assumed mass-loss rates and the need to develop a better theoretical understanding of stellar winds.