  The discovery over the last several decades of moderate luminosity AGNs in
disk-dominated galaxies - which show no "classical" bulges - suggests that
secular mechanisms represent an important growth pathway for supermassive black
holes in these systems. We present new follow-up NuSTAR observations of the
optically-elusive AGNs in two bulgeless galaxies, NGC 4178 and J0851+3926. NGC
4178 was originally reported as hosting an AGN based on the detection of [Ne V]
mid-infrared emission detected by Spitzer, and based on Chandra X-ray imaging
it has since been argued to host either a heavily obscured AGN or a supernova
remnant. J0851+3926 was originally identified as an AGN based on its WISE
mid-IR colors, and follow-up near-infrared spectroscopy previously revealed a
hidden broad line region, offering compelling evidence for an optically-elusive
AGN. Neither AGN is detected within the new NuSTAR imaging, and we derive upper
limits on the hard X-ray 10-24 keV fluxes of $<7.41\times10^{-14}$ erg
cm$^{-2}$ s$^{-1}$ and $<9.40\times10^{-14}$ erg cm$^{-2}$ s$^{-1}$ for the
AGNs in NGC 4178 and J0851+3926, respectively. If these non-detections are due
to large absorbing columns along the line of sight, the non-detections in NGC
4178 and J0851+3926 could be explained with column densities of
log($N_{\rm{H}}/\rm{cm}^2)>24.2$ and log($N_{\rm{H}}/\rm{cm}^2)>24.1$,
respectively. The nature of the nuclear activity in NGC 4178 remains
inconclusive; it is plausible that the [Ne V] traces a period of higher
activity in the past, but that the AGN is relatively quiescent now. The
non-detection in J0851+3926 and multiwavelength properties are consistent with
the AGN being heavily obscured.
