Most would cut the entire dried stalk to have a plant use it's energies more effectively for a better growing plant.
What sounds reasonable, If you have any coloring other than the dry coloring cut above the non dry coloring leaving some dry coloring. Although the whole dried stalk may need to be pruned off later in disregard to any off dry coloring.

Cut it closest to living tissue, Mister Tom. No, the stalk won't leaf out but the branch that it grew from should. Do you see any green bumps yet? None here so far, but then I've never had a flowering T here (holds back a winter-growing tear).

Non-Iron Man Jeff (since he has no starch)