Rubber plants like bright light, but never hot sun. Keep them out of drafts, and away from heat sources. Keep your plant evenly moist during the growing cycle in spring and summer, but on the dryer side during the rest of the year. They really appreciate having their leaves sponged off with a damp cloth. When you fertilize your rubber plant in the spring and again in early summer, use a weak mixture of a soluble house plant food.
Rubber plants have a tendency to lose their lower leaves, usually from environmental reasons.
If this happens very often, new shoots will emerge from the old leaf node. A very light nick, with a sharp,clean knife, right above the old node will often speed the new growth process from that point, but be sure to not cut to deeply. It sounds like there has been some sort of trauma to the plant, probably at the root level. Is it possible that it has become overwatered, causing the roots to rot. Yucca is also susceptible to root mealy bugs.