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.