Mobs can be spawned beyond the world border in old worlds

Mobs can be spawned beyond the old world border quite easily. 

In Creative mode, get a spawn egg and spawn mobs near the border. If you're lucky and get the angle just right, the mob will be dark and frozen outside the world. Hitting it will make it keep the red shade forever and effectively make it invincible. Interestingly, I somehow managed to get a dead mob beyond the border and it stayed in the death animation. I tried this on three worlds with Cows, Sheep, Mooshrooms and Cats and it worked semi-consistently, with variation based on entity pushing and spawn egg randomness.