Every egg that hatches was previously fertilized (at least for sexually-reproducing organisms). The animal that hatches from the fertilized egg became a genetically distinct organism when its egg was fertilized, not when the egg was hatched or laid.

In the case of chickens, eggs are fertilized (if at all) before being laid; and when we talk about “unfertilized eggs”, we usually mean eggs that were laid without being fertilized. Such eggs were not part of the discussion until you introduced them.

What’s your point? Unfertilized eggs don’t hatch, so they’re not part of the scenario in question.