Hi there - I saw this on Gardeners' World this week. A lady had one which was about 12' tall, but had been damaged by all the cold weather we'd had, they cut it down and said it would grow back again. When you do cut it down, see if the whole trunk has been affected by the softness you mention - if so, I dare say it's probably gone.....hope this helps.

Greenfingers, that was NOT a Yucca.
It was a Cordyline - the 2 plants are very very different and have different requirements.

Mcmullen, your Yucca will regenerate, they are tough plants and i doubt you've lost it.

I'm willing to bet your plant is, in fact, a Cordyline australis and not a Yucca - google for pics to check. If the trunk at the top is soft and soggy, check the rest of the trunk all the way down - you're looking for other soft and soggy areas or, worse, oozing white or orange gunk, often with a smell. If you find its all healthy apart from the top soft part, saw down beyond the soft part now, at an angle to allow rain to run off. If you find soggy areas lower down, saw down past those now. Then just wait - it should regrow from the roots.