Stray pets will only naturally spawn in Brindleton Bay and Selvadorada; unless you have a lot trait that allows stray cats or dogs to that lot, then they will spawn in that lot occasionally, but never in any other lots that aren't in those two worlds or without the lot traits. Two other traits that are Cat or Dog Friendly will spawn owned cats or dogs with their owners to visit the lot, however sometimes you won't even need the lot trait for a pet owner to show up to the lot with their pet; it will happen sometimes. Pet owners will never walk their dogs outside of Brindleton Bay, however.