  One of the primary goals when studying galaxy formation is to understand how
the luminous component of the Universe, galaxies, relates to the growth of
structure which is dominated by the gravitational collapse of dark matter
haloes. The stellar-to-halo mass relation probes how galaxies occupy dark
matter haloes and what that entails for their star formation history. We
deliver the first self-consistent empirical model that can place constraints on
the stellar-to-halo mass relation down to log stellar mass
$\log_{10}(m^*/\mathrm{M}_{\odot}) \leq 5.0$ by fitting our model directly to
Local Group dwarf data. This is accomplished by penalising galaxy growth in
late-forming, low-mass haloes by mimicking the effects of reionization. This
process serves to regulate the number density of galaxies by altering the
scatter in halo peak mass $M^{\mathrm{peak}}_{h}$ at fixed stellar mass,
creating a tighter scatter than would otherwise exist without a high-$z$
quenching mechanism. Our results indicate that the previously established
double-power law stellar-to-halo mass relation can be extended to include
galaxies with
$\log_{10}(M^{\mathrm{peak}}_{\mathrm{h}}/\mathrm{M}_{\odot})\gtrsim 10.0$.
Furthermore, we show that haloes with
$\log_{10}(M^{\mathrm{peak}}_{\mathrm{h}}/\mathrm{M}_{\odot})\lesssim 9.3$ by
$z=4$ are unlikely to host a galaxy with $\log_{10}(m^*/\mathrm{M}_{\odot}) >
5.0$.
