  A search for dark matter (DM) with mass in the sub-GeV region (0.32-1 GeV)
was conducted by looking for an annual modulation signal in XMASS, a
single-phase liquid xenon detector. Inelastic nuclear scattering accompanied by
bremsstrahlung emission was used to search down to an electron equivalent
energy of 1 keV. The data used had a live time of 2.8 years (3.5 years in
calendar time), resulting in a total exposure of 2.38 ton-years. No significant
modulation signal was observed and 90% confidence level upper limits of $1.6
\times 10^{-33}$ cm$^2$ at 0.5 GeV was set for the DM-nucleon cross section.
This is the first experimental result of a search for DM mediated by the
bremsstrahlung effect. In addition, a search for DM with mass in the multi-GeV
region (4-20 GeV) was conducted with a lower energy threshold than previous
analysis of XMASS. Elastic nuclear scattering was used to search down to a
nuclear recoil equivalent energy of 2.3 keV, and upper limits of 2.9
$\times$10$^{-42}$ cm$^2$ at 8 GeV was obtained.
