  Due to observational challenges our knowledge of low-level accretion flows
around neutron stars is limited. We present Nustar, Swift and Chandra
observations of the low-mass X-ray binary IGR J17062-6143, which has been
persistently accreting at ~0.1 per cent of the Eddington limit since 2006. Our
simultaneous Nustar/Swift observations show that the 0.5-79 keV spectrum can be
described by a combination of a power law with a photon index of Gamma~2, a
black body with a temperature of kT_bb~0.5 keV (presumably arising from the
neutron star surface), and disk reflection. Modeling the reflection spectrum
suggests that the inner accretion disk was located at R_in>100 GM/c2 (>225 km)
from the neutron star. The apparent truncation may be due to evaporation of the
inner disk into a radiatively-inefficient accretion flow, or due to the
pressure of the neutron star magnetic field. Our Chandra gratings data reveal
possible narrow emission lines near 1 keV that can be modeled as reflection or
collisionally-ionized gas, and possible low-energy absorption features that
could point to the presence of an outflow. We consider a scenario in which this
neutron star has been able to sustain its low accretion rate through magnetic
inhibition of the accretion flow, which gives some constraints on its magnetic
field strength and spin period. In this configuration, IGR J17062-6143 could
exhibit a strong radio jet as well as a (propeller-driven) wind-like outflow.
