It has previously been discovered that there is a universal power-law behavior exhibited by the late X-ray emission (LXRE) of a" golden sample" of six long energetic GRBs, when observed in the rest frame of the source. This remarkable feature, independent of the different isotropic energy (E iso) of each GRB, has been used to estimate the cosmological redshift of some long GRBs. This analysis is extended here to a new class of 161 long GRBs, all with erg. These GRBs are indicated as binary-driven hypernovae (BdHNe) in view of their progenitors: a tight binary system composed of a carbon–oxygen core (CO core) and a neutron star undergoing an induced gravitational collapse (IGC) to a black hole triggered by the CO core explosion as a supernova (SN). We confirm the universal behavior of the LXRE for the" enlarged sample"(ES) of 161 BdHNe observed up to the end of 2015, assuming a double-cone emitting region. We obtain a distribution of half-opening angles peaking at , with a mean value of , and a standard deviation of . This, in turn, leads to the possible establishment of a new cosmological candle. Within the IGC model, such universal LXRE behavior is only indirectly related to the GRB and originates from the SN ejecta, of a standard constant mass, being shocked by the GRB emission. The fulfillment of the universal relation in the LXRE and its independence of the prompt emission, further confirmed in this article, establishes a crucial test for any viable GRB model.