A lot of rescue dogs have ancestors that come from no formal breed at all. They were just local dogs adapted to local conditions and tolerated as long as they were useful and didn't bother anyone. We might have names for the type found in a locality: Desi dog, Potcake dog, Wadi dog, for example. A regional dog type might have a distinctive look that developed either by accident or because some trait was locally beneficial. However, these types haven't gone through the generations of artificial selection that would create a true breed.