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 can not 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 can not 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 .