I know humans and other animals start using their own proteins as food when starving. This made me wonder if a plant that is deprived of sunlight, after using up its sugar reserves and other carbs, could break down parts of its own woody structure in order to feed the rest of itself.
Googling yielded no useful results, which leads me to think the answer is no. I've never heard of plants themselves possessing cellulase, only certain animals.
Additionally, I would imagine that cellulose is not easy to transport, so it would have to be decomposed by the region of tissue surrounding it - which obviously couldn't last for long before that region died due to cannibalizing itself.