I have not heard of such a problem with bromeliads. It does sound like a varmint of some type. A fungus would cause a rot or decay. The possum seldom eats plants like that. If I were you I'd try peaking out at night at various hours to see what is doing this. Another option is to put a live trap out with some dog food in it to try and catch the culprit. Still another idea is to place the plants in an area that is muddy so the culprit would leave tracks when they come up to them.
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