Remove the succulent from its original container. Remove and discard all of the soil from around the roots. Discard or sanitize the container it grew in since it likely harbors fungi.
Inspect the plant and the roots for obvious signs of black stem rot, such as dark-colored, weeping spots or puckered flesh with a blackish tint around the edges. Cut off and discard any affected roots or stems with a gardening knife.
Set the succulent plant in a dry area with strong air circulation for two to three hours to allow the flesh and roots to dry out. Keep the succulent out of direct sunlight. Prepare a new planting container for the succulent while it is drying out.
Combine equal measures coarse sand, sterile loam and perlite to create a freely draining, porous soil mixture suited to caring for succulents afflicted with black stem rot. Use fresh, unused components when creating the soil mixture since previously used sand or soil may harbor pathogens.
Fill the bottom two inches of a clean, new planter with the soil mixture. Hold the succulent in the planter so the tips of the roots rest upon the surface of the soil. Backfill around the roots with the soil mixture until it reaches the base of the stems.
Firm the soil mixture around the base of the succulent to collapse any air pockets in the soil. Air pockets will trap moisture around the roots, which will cause further damage to the plant.
Set the newly potted succulent where it will receive warm temperatures, bright light and adequate air circulation. Avoid dim, closed-in locations where the succulent will be subjected to high humidity.
Water the succulent one week after re-potting it. Add only enough water to moisten the top inch of soil. Wait until the soil dries out completely before adding more water. Decrease water during the winter, adding only enough to keep the succulent from wilting.
Watch for the regeneration of healthy, green tissue where the blackish lesions once were about two months after re-potting the succulent.