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Shang Tsung lives on a secluded island. He causes problems and vanishes to his island so that people can't find or bother him.
Very few know of the location. If you manage to make it to the island, he will know of your appearance before you even step foot on it.
The one time that there was a tournament on his island, it was only because he needed a place. Other than that, he keeps his palace well-maintained and quiet.
His significant other would also live on the island with him. There is a special portal in one of the rooms so that his significant other can leave at any time and not be confined to the island. He wants them to stay safe away from everyone while maintaining their independence.