Hi Mark, When the leaf dies down dig it up.

As for the offsets. konjac produces rhizomatous offsets rather than offsets attached to the mother like paeoniifolius. You can cut them off at the mother tuber and in most cases the long runner will not last, but the small tuber at the end will be what grows next year. In zone 10 I'd just leave it in the ground and save the hassle to be honest :o) Dan