Yucca plant is still green and healthy leaves but where the old ones have been removed, the stems have grown out of shape and don't look nice at all. The plant is 20 years old and feel bad to throw it away, but it's not pretty to look at.
Bad Looking Yucca Plant
Certified GKH Gardening Expert
It is possible to prune off the the leafy top of the plant and propagate it.
You will have a shorter and more manageable plant.
Here is more information.