Seedling succulents should not be allowed to sit with exposed roots. However, many mature succulents can have exposed roots for up to a week while you allow the roots to dry out and prepare them for replanting.
Moreover, how do you keep a succulent stem from rotting?
Saving a Plant with Succulent Stem Rot
First, remove all signs of rot. Remove the leaves, and cut off the stem that has any rot. Then, look inside the stem you have remaining, to check for any signs of rot in the core of the stem. Continue cutting it back until all signs of rot are removed.
Keeping this in view, do succulent cuttings need sun?
Pick a location for your young succulents that gets bright, indirect light (not full, outdoor sun) and plenty of airflow. Cuttings need sunlight to grow new roots, but they can dry out quickly in direct sun.