A toy would have to be mutilated beyond being capable of being played with. If you watched the movie, Sid cuts off their heads, and limbs and that doesn't kill them. In the 4th movie a spork comes to life. Toys just don't die.
As you probably know, the Toy Story series is the prequel to cars, which may or may not force the humans to leave the planet. Then Wall-E brings them back, but they are incapable of caring for their planet and mutate into monsters who must travel back in time to collect screams or laughter from children in order to power their world, since the earths resources have been depleted.
That's the pixar one universe theory in a very nutty nut shell.