Is the area soft and mushy?? Just black but firm?? If it's mushy I would cut the entire portion off (to just below where you see the black). Sounds like you may have an issue with excessive moisture (combined possibly with inadequate HEAT). Are these in the ground?? In in the ground, I'd consider moving them into a container with very well-draining soil kept just slightly moist. Wait for the plant to begin to push vigorous new growth and then either increase pot size or move into the ground once temps get warmer for you. The situation for full recovery is not hopeless. Good luck!