  We report on a search for compact binary coalescences where at least one
binary component has a mass between 0.2 $M_\odot$ and 1.0 $M_\odot$ in Advanced
LIGO and Advanced Virgo data collected between 1 April 2019 1500 UTC and 1
October 2019 1500 UTC. We extend previous analyses in two main ways: we include
data from the Virgo detector and we allow for more unequal mass systems, with
mass ratio $q \geq 0.1$. We do not report any gravitational-wave candidates.
The most significant trigger has a false alarm rate of 0.14 $\mathrm{yr}^{-1}$.
This implies an upper limit on the merger rate of subsolar binaries in the
range $[220-24200] \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$, depending on the chirp
mass of the binary. We use this upper limit to derive astrophysical constraints
on two phenomenological models that could produce subsolar-mass compact
objects. One is an isotropic distribution of equal-mass primordial black holes.
Using this model, we find that the fraction of dark matter in primordial black
holes is $f_\mathrm{PBH} \equiv \Omega_\mathrm{PBH} / \Omega_\mathrm{DM}
\lesssim 6\%$. The other is a dissipative dark matter model, in which fermionic
dark matter can collapse and form black holes. The upper limit on the fraction
of dark matter black holes depends on the minimum mass of the black holes that
can be formed: the most constraining result is obtained at $M_\mathrm{min}=1
M_\odot$, where $f_\mathrm{DBH} \equiv \Omega_\mathrm{PBH} / \Omega_\mathrm{DM}
\lesssim 0.003\%$. These are the tightest limits on spinning subsolar-mass
binaries to date.
