I'm not too familiar with the basjoo, but you may want to top off the plant and allow for the new growth to emerge. I've had one or two where the leaves all start to die off and the new growth has kind of taken a dormancy, and topping it off and waiting about a month usually always seems to have done the trick for some of mine that have done this. Is this a pup attached to a mother, or pup removed, or a new plant that you just recently planted and what zone or area do you live in? Posting pictures would help to help you!

Good luck