Then they are the offspring of dogs that escaped or were abandoned long ago. Probably they also took over the population of any related species they can interbreed with.
That's an interesting historical and semantic question.
So there may not be any such thing as a "wild pigeon". Pigeons were domesticated so long and widely that all modern pigeons in the wild may be the feral descendants of ancient domesticated pigeons. But we still view modern pigeons as just a thing that exists out in the world.
If street dogs have been a self-sustaining population for long enough does that change their classification? What if the population of street dogs is older than many of the cities they inhabit? What if the population is thousands, ten thousand years old?
IMHO, the crucial point is whether they are populations that were wild all along (never domesticated) or whether they wholly originate from domestic dogs. But that's hard to say since domesticated dogs might have taken over the first group. Similar to how modern humans are hypothesized to have supplanted Neanderthals and other pockets of ancient human populations.
I’m not sure the exact answer, but one major difference between stray dogs and truly wild animals is that dogs typically can’t survive in the wild, they need to live near human settlements. This sets them apart from wolves (the nearest wild relatives of dogs).
So there may not be any such thing as a "wild pigeon". Pigeons were domesticated so long and widely that all modern pigeons in the wild may be the feral descendants of ancient domesticated pigeons. But we still view modern pigeons as just a thing that exists out in the world.
If street dogs have been a self-sustaining population for long enough does that change their classification? What if the population of street dogs is older than many of the cities they inhabit? What if the population is thousands, ten thousand years old?