I have had my fair share of lost pets. All of them took place when I was a kid. A pet turtle magically escaped and was gone for good. A few years later I saw a turtle at neighbor's and I thought it looked just like mine, but I didn't ask. A pair of parakeets opened the cage exit with their mouths and escaped overnight, or perhaps in the morning. They were never found.
My family only attempted to look for them in the neighborhood, and we did nothing more.
We have also had two parakeets flew into our home on two separated occasions in the past during the time I had my second pair of parakeets. So I ended up having total 4. O_O There was no way to find out their real owner. We only knew our nearby neighbors didn't have birds, so they must be from somewhere farther.