It is likely that the plant moves some material that it can scavenge out of the dying scape to reuse it to grow new leaves or other tissues. It does do this with dying flowers, and probably does the same thing with dying leaves. It should be slightly more beneficial to let the scape brown naturally and then remove it when a slight tug releases it from the crown. That would indicate that the process of exporting reusable resources from the scape had been completed.
