The story
From pavement + special (“thing which is distinctive or out of the ordinary”, noun), referring to the fact that stray dogs are often found roaming around on pavements.
Etymology from Wiktionary, CC BY-SA 4.0.
pavement special
pave·ment spe·cialToday it means: A dog (especially a stray dog) of miscellaneous ancestry; a mongrel, a mutt. Full definition →