  Motivated by the observed bottom-light initial mass function (IMF) in faint
dwarfs, we study how a metallicity-dependent IMF affects the feedback budget
and observables of an ultra-faint dwarf galaxy. We model the evolution of a
low-mass ($\approx 8 \, \times \, 10^{8} \, \rm M_{\odot}$) dark matter halo
with cosmological, zoomed hydrodynamical simulations capable of resolving
individual supernovae explosions, which we complement with an empirically
motivated subgrid prescription for systematic IMF variations. In this
framework, at the low gas metallicities typical of faint dwarfs, the IMF of
newborn stellar populations becomes top-heavy, increasing the efficiency of
supernova and photoionization feedback in regulating star formation. This
results in a 100-fold reduction of the final stellar mass of the dwarf compared
to a canonical IMF, at fixed dynamical mass. The increase in the feedback
budget is nonetheless met by increased metal production from more numerous
massive stars, leading to nearly constant iron content at $z=0$. A
metallicity-dependent IMF therefore provides a mechanism to produce low-mass
($\rm M_{\star}\sim 10^3 \rm M_{\odot}$), yet enriched ($\rm [Fe/H]\approx -2$)
field dwarf galaxies, thus opening a self-consistent avenue to populate the
plateau in $\rm [Fe/H]$ at the faintest end of the mass--metallicity relation.
