We have the exact same problem on both of our palms which are over 12 foot- they are in a very sorry state with virtually no leaves left and mushy branches/stems - still searching for the answer myself but will repost if I find out what to do. Wasn't sure if all hope is lost and they need cutting down??

there are so many poorly cordylines at the moment it would be interesting to know if any have survived ;o(

I have a cordyline which is seven to eight years old, and have thrived thru all winters except this one. Hard frost hit the crown of the plant which is now rendered useless. Best to replace with a new plant !!

You can try cutting the stem down by half in hopes that will force new growth from the base, or up the remaining stem. If no growth by end of May from anywhere, dig out and replace. If the stem is soggy when you cut it, get rid of it - Tesco and Wilkinson are selling these currently at £3 a pop.