  The NuSTAR Legacy program 'Unidentified INTEGRAL sources' targeted faint hard
X-ray sources revealed by INTEGRAL in the Galactic plane in order to provide
conclusive identification of their nature and insights on the population of
faint hard X-ray sources. The NuSTAR and Swift/XRT observations obtained in
2015-2017 contributed to the successful identification of five persistent
sources. Here, we report on the spectral and variability analyses which helped
to consolidate the classifications of IGR J10447-6027, IGR J16181-5407 and IGR
J20569+4940 as active galactic nuclei, and IGR J17402-3656 as an intermediate
polar. An optical spectrum of the blazar IGR J20569+4940 is also presented.
Combining these results with successful identifications of other such faint and
persistent INTEGRAL sources reported in the literature, we investigate possible
implications for the population of persistent high mass X-ray binaries (HMXBs)
below the identification completion limit of the INTEGRAL survey. The current
trend hints at a deficit of persistent HMXBs below $F_{\rm 17-60keV} =
10^{-11}$ erg cm$^{-2}$ s$^{-1}$, but additional efforts dedicated to
classifying faint hard X-ray sources are needed before we can draw solid
conclusions.
