The diff is mounted securely without the need for the drivershalf or output shalf to be attached, they are not supporting any of the weight of the diff.
I find it every hard to believe your assessment. Although likely, i think it were more parts of failure and rather the driveshalf and outshalfs is a symptom not the source of the problem.
I would first check all other mounting points of the diff. If the diff wasn't properly mounted or a few of the bolts came off, the rear mount would be the only thing holding it and it would eventually break off.
I would also check all your rear subframe mounting points, they have a history to tear apart on e36s. If your rear sub-frame came apart and is loose enough I can see how that would put alot of pressure on the diff, snapping the mount.
Once you get that car on a hoist, it would be pretty easy to tell what happened.