  We present a comprehensive X-ray study of the neutron star low-mass X-ray
binary IGR J17062-6143, which has been accreting at low luminosities since its
discovery in $2006$. Analysing NuSTAR, XMM-Newton and Swift observations, we
investigate the very faint nature of this source through three approaches:
modelling the relativistic reflection spectrum to constrain the accretion
geometry, performing high-resolution X-ray spectroscopy to search for an
outflow, and searching for the recently reported millisecond X-ray pulsations.
We find a strongly truncated accretion disk at $77^{+22}_{-18}$ gravitational
radii ($\sim 164$ km) assuming a high inclination, although a low inclination
and a disk extending to the neutron star cannot be excluded. The
high-resolution spectroscopy reveals evidence for oxygen-rich circumbinary
material, possibly resulting from a blueshifted, collisionally-ionised outflow.
Finally, we do not detect any pulsations. We discuss these results in the
broader context of possible explanations for the persistent faint nature of
weakly accreting neutron stars. The results are consistent with both an
ultra-compact binary orbit and a magnetically truncated accretion flow,
although both cannot be unambigiously inferred. We also discuss the nature of
the donor star and conclude that it is likely a CO or O-Ne-Mg white dwarf,
consistent with recent multi-wavelength modelling.
