There are definitely people who tend to be emotional sponges. They basically suck everything out of you until there is nothing left. If you try to support them emotionally, you find that they are basically a bottomless pit. No matter how much of yourself you give, it is never enough. As you say, this is because there is something missing or broken in them that they look to you to solve, but which no one but themselves can actually solve. I have personally been around such people and my best advice is to get away as soon as you can.
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You hit the nail on the head!