  Context. It has been proposed that the temporal coincidence of a gamma-ray
burst (GRB) and a type Ib/c supernova (SN) can be explained with the concept of
induced gravitational collapse (IGC), induced by the matter ejected from an SN
Ib/c accreting onto a neutron star (NS). The NS is expected to reach the
critical mass necessary for it to collapse to a black hole (BH) and emit a GRB.
We found a standard luminosity light curve behavior in the late-time X-ray
emission of this subclass of GRBs. Aims. We test if this standard behavior in
the luminosity found in this subclass of GRBs can become a redshift estimator
of these sources. Methods. We selected a sample of GRBs that belong to this
subclass of IGC GRBs associated to an SN (IGC GRB-SN sources). These sources
have an isotropic energy $E_{iso} > 10^{52}$ erg and their cosmological
redshifts are in the range of $z = 0.49-1.261$. We focused on the corresponding
X-ray luminosity light curves. Results. We find that all GRBs of the sample
with measured redshift present a standard luminosity late-time light curve in
the $0.3-10$ keV rest-frame energy range. We used these results to estimate the
GRB redshift of the sample without a measured redshift and found results
consistent with other possible redshift indicators. Conclusions. The standard
late-time X-ray luminosity light curve of all GRBs of the sample shows a common
physical mechanism in this particular phase of the X-ray emission, possibly
related to the creation of the NS from the SN process. This scaling law
moreover represents strong evidence of very low or even absent beaming in this
late phase of the X-ray afterglow emission process. This could be a fundamental
tool for estimating the redshift of GRBs that belong to this subclass of
events. We are currently expanding this subclass of GRBs to further verify the
universal validity of this new redshift estimation method.
