Very rare winged dog???
Kind of reminds me of that silly verse from childhood:
"I saw a seagull in the sky
It dropped some whitewash in my eye...
Gee, I'm glad that cows can't fly!"
Seriously, how high is the fence? Have you checked for signs of digging under it? Could the poop be from a different kind of critter, like a raccoon, that can climb easily? Could someone have left the gate open and then later remembered it and closed it, but said nothing? Could you have a malicious neighbour, adult or child, who flung it over the fence?