Actually it's best to not dress the wound. You want it to dry and callous over quickly and dressing it will slow down this process. Jades are very easy to grow and will survive harsh pruning with no attention to the pruning cuts. Just provide ample light and good air circulation and the wounds should heal over just fine on their own. About the only thing that will kill a Jade is overwatering. They prefer to go just about bone dry before being given a thorough soaking.

air circulation is going to help the most. is it indoors or out? make sure your soil is low on peat and high on grit. if you want to cut this branch, leave about an inch so that this will dry up and fall off and not leave a bump. i've heard of people using a fungicide powder, but i worry without good air flow it would only make things worse. get an oscillating fan set on low if it is indoors. hope everything works out. if it doesn't look like it's getting better, chop it clear to the soil line (okay maybe leave a few inches). It will come back, even with no leaves. good luck.

I would unpot the plant, remove as much of the existing soil as possible, and let the plant dry out (outside in the shade if past your frost free date) for a week. When you repot, use a clay pot no bigger than the root mass, and do NOT put pebbles or anything similar at the bottom. Simply cover the drainage hole with a piece of paper towel. Use a coarse soil mix to repot (add an equal amount of perlite to a Cactus mix), and don't water for another week, and then only a little until you see active growth. Take some cuttings in case the main plant doesn't make it!
Good growing to you!

Did you put it back in the same pot? It sounds like it might be a bacterial/fungal infection, which could remain in the pot and then reinfect the soil and the plant, if that is indeed what it is. Good luck

Thanks so much for the info! I sat a fan on it this morning. Any opinons on using baking soda to rid bacteria and fungus? The main trunk is about 5 inches in diameter. Would break my heart to have to cut through it. Wish me luck. Thanks again!

im wondering why rjm says not to crock it. I crock almost everythign i have. anyhow, I had a branch suddenly go limp and after removing it, the rest of the plant seemed unaffected. I didnt dress the wound. Im guessing it is some other type of rot and ill agree with the suggestion of taking it out, removing the dirt again and put into a new pot. I prefer clay. good luck!

If crocking it means putting pebbles or rocks in the bottom of the pot (under the mix) in the hopes of helping drainage, I've heard/read that the latest thinking on that is that it doesn't help, can actually impede drainage instead.

Why baking soda? I've never heard of this & it's alkaline so may do damage to the plant. If an antifungal is what you want, either use a rooting hormone w/ fungicide (using it in this case only for the fungicide), or try brushing on some plain cinnamon on the cuts where the rotting sections were or the fungus is. Cinnamon is a natural anti-fungus, I learned of this from Orchid growers.