When I saw the topic of the thread I thought it was about a pet passed away.
While I haven't lost any pet recently, many years ago I had parakeets somehow opened the exit of their cage and disappeared into the neighborhood. I do not believe they are among the bird species recognize their way home. Back then I was only a kid, and I was so worried about their well being since I doubt they could have survived on their own. Sure they can chew on various plants as veggie is a part of their diet, but seeds are hard to come by in a city where I used to live. Hopefully someone found them and took good care of them.
@ Corzhens,
Are you sure the pigeon left you at free will? Maybe she got lost, maybe she was in some kind of trouble and unable to go back to you. The only thing we know is that she did not come back. Anyway, I am sorry to hear about it. I hope she is doing well either on her own or maybe with another family who also takes good care of her just like yours.