I'm probably 90% against existence, but withhold 10% chance. Again, I am not a badass outdoorsman-'Great White Hunter'-type dude. But I have spent a considerable amount of time sleeping on the ground, and have never once come across a bear carcass for instance. Unless an animal was killed by predation- I haven't ever found it's remains and that includes mountain lion, wolves, bear, coyotes, or even a fox.
There are several photos of what appears to be a large predatory cat in the UK for instance, yet no remains have been found. Hell, people in Kansas say they've seen mountain lion/large cats and I remember as a kid down in Arkansas folks saying the same thing. Yes, those animals are known to exist and it isn't beyond imagination that a few might be roaming outside their range. But every now and then you read about the discovery of large animals/fish in the ocean that were thought to be extinct for 2 million years...recently a certain whale if I am not mistaken. All this is the open-minded ten percent side of me.
The overwhelming majority agrees that somehow, somewhere a person would have killed one and either cut a piece off, or gotten a very good up close photo.
Interesting if nothing else.