If you can bear to, wait till spring and chop it right down- this might have the effect of forcing new growth from the roots - if it doesn't then remove it, but wait till end of June - sometimes it takes that long to show new growth. If you don't like the look of it, just take it out - I'd have expected some baby growth at the base this year were the roots still okay.

I had 2 very big ones that did not survive last winter.One of them has now thrown up 5 babies!Will leave them to it this winter.I cut down the old trunks which were very thick.Other one is completely dead.Best of luck with yours

Thanks for the advice. I had a couple of babies that sprung out of the bottom in summer but they seem to have died too. I'll hold on till spring and see if there is any improvement.