Kill your pet cat or dog (starve it, burn it, etc.). When the Grim Reaper arrives, plea and hopefully lose. If you win and the pet lives, kill it again. Once you lose, the Grim Reaper will turn it into a zombie. Your undead pet will still want to be fed, rested, and cleaned but will not die if you do not do those things. Note: You can still train and interact with your pet.