This thread is really old (2015), it is usually better to start a new one. But here are few questions: why the part of plant fell off - did it just break because some mechanical/physical happening or it 'fell' off because of rotting? If healthy, I would take off few very bottom leaves to have bit of stem and stick it into fast draining mix. Warning: I never rooted this plant, but have some cuttings and am going to do exactly what I said, hoping it will work :) Black spots on the leaves look fungal to me - what kind of soil/mix is it potted in? Is there a drainage hole in container? What kind of ligh is plant receiving?

Aside from the " theory" which also fails as often as it works I've attepted to re- root a rootless jade VIA root rot in brighter sun little/ no watering with no sucsess. You have better chances as mentioned from greenman all it really needs for root is brightness and warmth. Understand the full sun brightness is indeed bright ( Re your posted pics) but it's brightness is alot closer to heat than it is to warmth. A stressd plant such as yours should be kept cooler Here I use 70 F as an avg high with cooler inside brightness during the heat of the day with better sucesses than outside. Yours is dimishing it's stored water fatser in the warmer direct sunlight brightness . Cooler brightness with less direct warmer full sun would help it's stored moisture be reserved longer increasing root re-establishing possibilaties to be better. Granted it may have to loose a growing season ( or two) Better doesn't mean faster cause the other theory is if anything can go wrong it will and when it does go wrong it continues to go wrong faster than we can win the fix faster race. Slow it down so when things do go wrong at least it takes longer for it to go wrong allowing more time to fix it slower.

I'm no expert, but while you have the plant out of the pot I would wash the dirt off the roots. Then I'd check them and the lower stem for rot (black and squishy). If there is any rot it will need surgery. There are many threads on cutting off rot from roots/stem/leaves and how far to cut. You could do a search on rot. But if you suspect rot take a photo of the plant showing the affected areas and people can guide you through. If it needs rerooting this is a helpful thread about beheading plants and rerooting. http://forums.gardenweb.com/discussions/4611851/beheading-plants?n=58 As I said I'm no expert and I may be saying all this when not needed. I hope thats the case :-)

Your mix could be water-retaining. I can't really judge, I do not use mix with 50% soil in it. That doesn't mean mix that is 50/50 doesn't work. I do not have same plant (Crassula rupestris), but have Crassula Moonglow which could have similar growing needs (?) I decapitated it, and also cut into few pieces, and all parts rooted and are growing. Bunkfree also showed hers (posted on May 2, 2017; June 4 and few more), and also C. perforata in -BEHEADING THREAD- . Pls. check all comments, and also beheding thread #2 (link at the end of #1) for photos and comments. Many cuttings were rootless, and rooted well. I use mostly inorganic mix, but particles are much more uniform. Some photos Bunkfree posted show more 50/50 mix - so I do not see that much difference or need to use most or all pumice. I use smaller pots, sometimes maybe even too small. Reason is mainly space since I have to many plants.