  We estimate the feeddown contributions from decays of unstable $A = 4$ and $A
= 5$ nuclei to the final yields of protons, deuterons, tritons, $^3$He, and
$^4$He produced in relativistic heavy-ion collisions at $\sqrt{s_{\rm NN}} >
2.4$ GeV, using the statistical model. The feeddown contribution effects do not
exceed 5% at LHC and top RHIC energies due to the large penalty factors
involved, but are substantial at intermediate collision energies. We observe
large feeddown contributions for tritons, $^3$He, and $^4$He at $\sqrt{s_{\rm
NN}} \lesssim 10$ GeV, where they may account for as much as 70% of the final
yield at the lower end of the collision energies considered. Sizable ($>10$%)
effects for deuteron yields are observed at $\sqrt{s_{\rm NN}} \lesssim 4$ GeV.
The results suggest that the excited nuclei feeddown cannot be neglected in the
ongoing and future analysis of light nuclei production at intermediate
collision energies, including HADES and CBM experiments at FAIR, NICA at JINR,
RHIC beam energy scan and fixed-target programmes, and NA61/SHINE at CERN. We
further show that the freeze-out curve in the $T$-$\mu_B$ plane itself is
affected significantly by the light nuclei at high baryochemical potential.
