The progenitor evolution of the the massive X-ray binary Wray 977 is investigated using new models of massive close binary evolution. These models yield constraints on the mass limit for neutron star/black hole formation in single stars, M-BH. We argue for quasi-conservative evolution in this system, and we find M-BH > 13..21 M-. from the existence of a neutron star in Wray 977, with the uncertainty being due to uncertainties in the treatment of convection. Our results revise earlier published much larger values of Msw derived from the parameters of Wray 977. Then, on the basis of a grid of 37 evolutionary models for massive close binaries with various initial masses, mass ratios and periods, we derive primary initial-final mass, initial mass-final helium core mass, and initial mass-final CO-core mass relations for the various mass transfer cases of close binary evolution. From these models we derive for single stars that M-BH less than or similar to 25 M-., independent of whether most black hole binaries formed through the Case A/B or the Case C binary channel. Using our grid of binary models, we obtain a consistent scenario for the formation of black holes in binary systems. We emphasize that in binaries the critical initial mass limits for neutron star/black hole formation and for white dwarf/neutron star formation are very different from the corresponding values in single stars. While the first may well be above 100 M-. in Case A/B binaries, the latter is found to be in the range 12...15 M-. instead of the canonical value of 8...10 M-. usually quoted for single stars. This effect should not be neglected in population synthesis studies of massive binary systems. Also, neutron star and blade hole mass functions obtained for single stars cannot per se compared to the masses of compact objects in binary systems. Massive close binaries produce also Type Ib and Ic supernovae, We find two different types of supernova progenitor structure in our models, one with remaining helium masses of the order of 1 M-. which stems from an intermediate progenitor initial mass range (about 16...25 M-.), and another with one order of magnitude smaller remaining helium masses from initial masses above and below this. A possible connection to the distinction of Type Ib and Type Ic supernovae, and implications from the Type Ic supernova SN1998bw and its associated gamma-ray burst are discussed.