Thank you for the question. Generally, jade plant or Crassula arborescens is an easy to maintain. The advanced age of your plant proves this to be true but clearly, there is something wrong.   The fact that you have successfully cared for it for many years without problems leads me to believe that the plant has been cared for properly with sufficient light, warmth, and watered only when soil is dry. From the photos, it appears that some of the upper leaves are healthy, but the lower down on the stem toward the soil, the leaves wrinkle and the stems are dying. I can't tell if there is disease or insect problems but will provide some links so that you can examine your plant carefully and compare to descriptions. While insects and diseases can certainly cause problems, light and water problems are the most common reasons for houseplant failure. Make sure that the drainage holes of the pot are not blocked which would cause the plant to sit in water and lead to root rot. Plants can become root bound and block the drainage of water. If the roots are rotting, water and nutrients can't travel up the stem and you would get die back and wilting leaves. Of course, too little water but healthy roots would lead to the same thing. In such an old plant, you might be wise to start some new jade plants from the leaves that are putting roots out into the air.  

You should knock the plant out of the pot, examine the roots, and take corrective action. It may need to be replanted or have dead roots pruned off. If you find evidence of disease, treat as recommended in the publications below.

Please read these publications on the proper care of houseplants and identification/resolution of problems:

https://www.ag.ndsu.edu/extensionentomology/urban-and-forestry-insect-pests/documents/homes/pp-744-houseplants-proper-care-and-management-of-pest-problems-december-2009

 https://extension.psu.edu/preventing-diagnosing-and-correcting-common-houseplant-problems

This is our publication on cacti and succulents which you might find useful:

Thank you for contacting Extension.