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The Bible's teaching on zombies is the same as its teachings on warewolves and vampires... which is.... wait for it.... nothing!
The reason for this alarming ignorance to these menaces in Scripture is due to the one little snag we face in that they're fictional creations and don't exist in reality.
The reality is our body will be vanish but our spiritual is the unreality who are going to live and return to its belong.
So, the question is; whether we put real or unreal in our daily life?