WillC said:The canes of your Yucca are dying and already beyond recovery. In a desperate effort to hang in there, it is sending out a small, suckered growth from the base of the cane just under the soil. These suckered growths rarely make it when left as they are.
You might try digging into the soil a bit and severing it from the cane and include any roots that seem to be attached to it. Pot it into a very small 3 or 4-inch pot with a porous potting mix. Keep the soil just barely damp and the plant in a sunny location.
The main canes are no longer viable and should be discarded. Hard to say what caused their demise but it was either not enough light (it needs lots of direct indoor sun) or improper watering.