First of all. This is not an elephant Bush (portulacaria affra), but a crassula ovata. Both of them is sometimes called jade plants, wich easily gets confusing. Anyway, the care is the same.
Your tree has been overwatered at some time. Or really, watered too often not too much. It is very important that this species dries up quickly after watering and stays dry for quite a wile in between. The best way is to have a very well draining soil and soak it really good when watering.
My jades kept in frost free greenhouse stays bone dry from early authum to mid spring without no watering whatsoever. The rest of the year they gets a good soak every 2-3 weeks. Only increasing to once a week in the peak of the summer. Local conditions can demand other frequency. I live in Western Sweden but still the greenhouse is up to 35 degrees daytime most of the summer.
I have one more mature tree out on the benches in the summer. That one I never water, but rely on summer rain only. Works good as well.
This kind of rot is hard to stop. I would suggest cut healthy cuttings and start them from scratch. When done you can try to cut all rotten tissue and dispose. Keep the tree dry until there are signs of backbudding. If grown healthy during the season you can try to repot into better substrate in a year.
But as said, it is hard to stop once started. Good luck!