  Most massive stars are born in binary or higher-order multiple systems and
exchange mass with a companion during their lives. In particular, the
progenitors of a large fraction of compact object mergers, and Galactic neutron
stars (NSs) and black holes (BHs) have been stripped off their envelopes by a
binary companion. Here, we study the evolution of single and stripped binary
stars up to core collapse with the stellar evolution code MESA and their final
fates with a parametric supernova (SN) model. We find that stripped binary
stars can have systematically different pre-SN structures compared to genuine
single stars and thus also different SN outcomes. The bases of these
differences are already established by the end of core helium burning and are
preserved up to core collapse. We find a non-monotonic pattern of NS and BH
formation as a function of CO core mass that is different in single and
stripped binary stars. In terms of initial masses, single stars of >35 Msun all
form BHs, while this transition is only at 70 Msun in stripped stars. On
average, stripped stars give rise to lower NS and BH masses, higher explosion
energies, higher kick velocities and higher nickel yields. Within a simplified
population synthesis model, we show that our results lead to a significant
reduction of the rates of BH-NS and BH-BH mergers with respect to typical
assumptions made on NS and BH formation. Therefore, we predict lower detection
rates of such merger events by, e.g., advanced LIGO than is often considered.
We further show how features in the NS-BH mass distribution of single and
stripped stars relate to the chirp-mass distribution of compact object mergers.
Further implications of our findings are discussed with respect to the missing
red-supergiant problem, a possible mass gap between NSs and BHs, X-ray binaries
and observationally inferred nickel masses from Type Ib/c and IIP Sne.
[abridged]
