They are simply waiting to eat your face off.
1stholistic.com has an article that spreads the biggest misconception I've come across.
The Daily Mail has a version of the story that makes the concept seem a bit more acceptable- The pet had run out of food and as a last choice, fed off it's master to stay alive.
There are many misconceptions and crackpot stories surrounding death. No wonder, people spend so much time avoiding the thought that any junk story can fill the vast gaps in our conceptualization of the topic. I'm here to set the story straight. Your pet would likely at least take a few bites if left alone with your dead body, even after a fairly short amount of time. I've seen it.
I had one case where a medium sized mutt, who had allegedly been walked every day by his master and fairly well cared for, had been trapped in their trailer with the dead master for about a week. The head was pretty much cleaned of all flesh and was sitting next to the body, the lower mandible was on the floor, and the teeth were spread all across the carpet. Trust me, it was a ton of fun looking for those teeth. The right arm had been separated from the body as well. Here's the kicker. There were two 40 lb paper bags of dog food on the floor in the kitchen. Both were full and one was open, totally within reach of the dog.
I didn't do anything wrong!
I had another case where I stepped into a bedroom to see a male's body on it's bed, missing half his face with the cutest little pug darting about on the bed, scared, and trying to keep me away from the body. We got the little guy into a carrier and gave him to family who were going to care for him. He had a bowl of water and uneaten food in the neighboring bowl on the floor.
And yes I have seen cats do the same thing, but the damage was usually limited to the nose, mouth, and fingers.
WTF? Why would our cute little babies do such a thing? I have a hypothesis. I think that the animals are doing an extension of what they already do. How many times has your pet attempted to wake you with a nose in the face, a big sloppy lick, or a gentle paw pat to the nose? I've been woken up in that manner many times. Now imagine if the pet is trying to wake you and you don't wake up after the normal gentle prodding. My dog usually growls loudly or even barks, that generally tends to piss me off enough to at least wake up enough to yell "shut up!". But what if that didn't work? I think cats might resort to a swat with claws extended- I've definitely seen that damage. a dog might be tempted to nip at you. I think you get the idea. Over time, the animal gets more distressed and the nipping and clawing progresses to full on bites. I know that once a dog gets it's mind set in one direction, it will keep going unless something is there to stop the behavior.
In both cases of the dogs, they were adopted off, not put down. I don't think there is such a thing of "getting the taste of human flesh" that is different from a dog that has attacked a live human.