Unfortunately, you haven't said what kind of palm it is, whether its a cordyline or not, and the picture only shows the base - you say its "dormant" this year, if it is a cordyline, it may well have been killed off or badly damaged by last winter - the growth at the bottom is coming from the roots, and may have appeared to replace the rest of the tree, growing on in the same way. I'm also not sure what you mean by "dormant" - if you mean dead, then you may want to cut the trunk off at the base, but, as I said, I'm not advising that for definite because I don't have enough info on your palm.