Negative displacement comes from negative numbers. If you use a math node to subtract a constant from the displacement map, you can make part of it positive and part of it negative. Or you can make it entirely negative as I've done here.

The transparency you see indicates where the original geometry position was.

Observe the red line is below the black line on the lower left. That's a graph of the displacement amount - all below the black line means all negative displacement.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)