Many young, massive stars are found in close binaries. Using population synthesis simulations we predict the likelihood of a companion star being present when these massive stars end their lives as core-collapse supernovae (SNe). We focus on stripped-envelope SNe, whose progenitors have lost their outer hydrogen and possibly helium layers before explosion. We use these results to interpret new Hubble Space Telescope observations of the site of the broad-lined Type Ic SN 2002ap, 14 years post-explosion. For a subsolar metallicity consistent with SN 2002ap, we expect a main-sequence (MS) companion present in about two thirds of all stripped-envelope SNe and a compact companion (likely a stripped helium star or a white dwarf/neutron star/black hole) in about 5% of cases. About a quarter of progenitors are single at explosion (originating from initially single stars, mergers, or disrupted systems). All of the latter scenarios require a massive progenitor, inconsistent with earlier studies of SN 2002ap. Our new, deeper upper limits exclude the presence of an MS companion star> 8–10