Black roots are generally rotted due to excessive watering, and bacteria may invade. Still sprouting, indicating that his main stem is not dead, but living on the nutrients of the main stem. Most succulents are basically like this. You can dig it up and have a look. If the root is really rotten, you can cut off the black part of the lower part with a sharp knife, then dry the wound in natural air (there is no liquid in the neck), and then plant it in the soil after there is a film on the cut surface. Don't pour too much water to prevent it from rotting again. It is best to use new soil or old soil after disinfection. It's just that the new cuttings of keel are not easy to survive in winter, and the survival rate of new branches is higher than that of old branches. If there are many branches, you can break off one or two small branches, soak them in water, take root in water, and then plant them in soil, which has a higher chance of survival. I often reproduce in this way. You can try. Good luck!