May I just add that you need to remove any smooshey parts of the plant to keep the rot from spreading. Use a clean sharp knife to remove small sections of stem at first, so you can assess the damage before going too deep. Even a tiny area of rot that is left behind will spread and grow, so if you are in doubt, cut a little deeper.
Any pieces that you remove can be rooted if the damage area is removed... With patience and little effort, even single leaves can be turned into very cute 'Micro Jades' that will grow and thrive and impress your friendshttp://www.thegardenhelper.com/jade.html
(there are several more Jade care links at the bottom of that page)