Do you perhaps mean wolves by strays? If so,, I don't think that's how natural evolution works, otherwise humans might start looking like Homo erectus.

The main distinction between an actual 'stray' dog and a domestic dog is environmental, being around humans and so on and less to do with genetics.

If you let dogs breed freely they'd probably still clump into sets of similar genetic and physical traits based on time and location (and their prior genetics).