  We present a population of 11 of the faintest ($> 25.5$ AB mag) short
gamma-ray burst (GRB) host galaxies. We model their sparse available
observations using the stellar population inference code Prospector-$\beta$ and
develop a novel implementation to incorporate the galaxy mass-radius relation.
Assuming these hosts are randomly drawn from the galaxy population and
conditioning this draw on their observed flux and size in few photometric
bands, we determine that these hosts have dwarf galaxy stellar masses of
$7.0\lesssim\log(M_*/M_\odot)\lesssim9.1$. This is striking as only $14\%$ of
short GRB hosts with previous inferred stellar masses had $M_* \lesssim
10^{9}\,M_{\odot}$. We further show these short GRBs have smaller physical and
host-normalized offsets than the rest of the population, suggesting that the
majority of their neutron star (NS) merger progenitors were retained within
their hosts. The presumably shallow potentials of these hosts translate to
small escape velocities of $\sim5.5-80$ km/s, indicative of either low
post-supernova systemic velocities or short inspiral times. While short GRBs
with identified dwarf host galaxies now comprise $\approx 14\%$ of the total
Swift-detected population, a number are likely missing in the current
population, as larger systemic velocities (observed from Galactic NS
population) would result in highly offset short GRBs and less secure host
associations. However, the revelation of a population of short GRBs retained in
low-mass host galaxies offers a natural explanation for observed $r$-process
enrichment via NS mergers in Local Group dwarf galaxies, and has implications
for gravitational wave follow-up strategies.
