Cats and Dogs are much more acidic than humans - they can eat meat that we may see as rotten. So, even meat left out for a few days can be ok, especially if you have a garden and put the meat in the shadiest spot, and then cover with some leaves/sticks .. animals like to find their food.
I feel my dog an all raw diet, and what I have found is that if I give him too much, he ends up burying some, and digs it up a few days later when he's peckish.
I have read of people who gave their animals no food for several days, and then the animals were so hungry they were happy to move straight into eating raw ... maybe that's a way?