I had a cordyline which got to about seven feet in height. The last very cold winter killed the crown, but I noticed new growth was appearing around the bottom of the trunk. I decided to get rid of it, but had I decided to keep it, I would have cut it back to the bottom, where the new growth had started, and I believe it would have been ok. If you do the same, it may be ok, if not, then get rid of it, I suggest.