Can you post us a photo, Richard? Normally if the growing tip gets damaged, they just make new ones on the sides a little lower down. If yours broke so low that never generated new bud tissue (this sounds possible due to yours having been damaged /three/ years ago) then you will probably have to graft one or more stem pieces to it that contain bud tissue. Otherwise it is possible that the caudex will otherwise remain without leaves or branches. Sometimes people take root cuttings and the same thing happens.

In most plants new bud tissue can be formed almost anywhere. But as an adenium caudex has chlorophyll in the stem, it can survive much like a cactus - without leaves.