That's got to be pretty rare. I've been impressed with the typical differential mounting scheme.
Did it literally fall off the car (totally)? Fall down and start scraping the road? Or did you completely strip out the gears and are unable to move?
Does it seem like the bolts broke or the nuts fall off? If yours is the typical design, it has four large studs coming out of the top of the differential and is held on by four self-locking nuts.
I bought a used differential for the 1982 300D for $135 from Potomac German auto. They can be shipped. Nothing wrong with a used differential if you have the opportunity to check it somehow yourself or have return rights if it is worn. The main checks to perform on a used unit are the condition of the rubber seals for the pinion and axle shafts, and to look for any looseness in the gearing. You turn the driveshaft flange back and forth and make sure the axle shaft recepticals match that movement without much (if any) slack. Mine came from a 1985 300D with about 85k miles - just like new condition.
1982 300D at 351K miles
1984 300SD at 217K miles
1987 300D at 370K miles