Hi
@Sharonrammel,

to the site!
It may just be my eyesight but I don't see any rot on the stems of your
Christmas Cactus (Schlumbergera truncata), only what looks like normal wood. With age, Schlumbergera species will form a woody base and in time can become 3 to 4 foot shrubs.
You can see some of the woody stems on the right side of my Schlumbergera in this photo: