  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 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 the latter scenarios require a massive progenitor, inconsistent
with earlier studies of SN 2002ap. Our new, deeper upper limits exclude the
presence of a main-sequence companion star $>8$-$10$ Msun, ruling out about 40%
of all stripped-envelope SN channels. The most likely scenario for SN 2002ap
includes nonconservative binary interaction of a primary star initially
$\lesssim 23$ Msun. Although unlikely ($<$1% of the scenarios), we also discuss
the possibility of an exotic reverse merger channel for broad-lined Type Ic
events. Finally, we explore how our results depend on the metallicity and the
model assumptions and discuss how additional searches for companions can
constrain the physics that governs the evolution of SN progenitors.
