I have not heard of self-fertilized eggs, but unfertilized eggs sometimes can develop. If you want to search and read about it, try using the term "parthenogenesis."I understand of all the rarities a chicken that could lay a self fertilized egg has never happened. Although I believe one of the members didn't mention an article and that article talked about quail laying self fertilized eggs.
Here is an article that talks a bit about the subject, and mentions research that was done some years ago:
https://www.thepoultrysite.com/arti...-normal-fertilization-and-embryonic-mortality