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According to theory, the torus of active galactic nuclei (AGN) is sustained from a wind coming off the accretion disc, and for low efficient AGN, it has been proposed that such structure disappears. However, the exact conditions for its disappearance remain unclear. This can be studied throughout the reflection component at X-rays, which is associated with distant and neutral material at the inner walls of the torus in obscured AGN. We select a sample of 81 AGNs observed with NuSTAR with a distance limit of D< 200 Mpc and Eddington rate |$\rm {\lambda _{Edd} \equiv L_{bol}/L_{Edd}\lt 10^{-3}}$|⁠. We fit the 3–70 keV spectra using a model accounting for a partial-covering absorber plus a reflection component from neutral material. We find that the existence of the reflection component spans in a wide range of black hole mass and bolometric luminosities, with only ∼13 per cent of our sample (11 sources) lacking of any reflection signatures. These sources fall in the region in which the torus may be lacking in the L-MBH diagram. For the sources with a detected reflection component, we find that the vast majority of them are highly obscured (⁠|$\rm {\log \ N_H \gt 23}$|⁠), with |$\rm {\sim 20{{\ \rm per\ cent}}}$| being Compton-thick. We also find an increase in the number of unobscured sources and a tentative increase on the ratio between |$\rm {FeK\alpha }$| emission line and Compton-hump luminosities toward |$\rm {\lambda _{Edd}=10^{-5}}$|⁠ , suggesting that the contribution of the |$\rm {FeK\alpha }$| line changes with Eddington ratio. [ABSTRACT FROM AUTHOR]