It's so rare, but it actually does happen, and the people doing it actually try to conceal it like a half eaten sausage that "just fell".

But this isn't even about this particular half eaten sausage. A dog doesn't know the difference between a pristine sausage and a half eaten one, to them it's just meat. And the point is that dogs should be taught to never eat any meat on the street - because they can't think "uh, looks half eaten, probably fine".