Yes, something is wrong, and probably has been since before you got the car because you wrote, "...My brakes have always been soft, but I assumed it was due to the ABS; until recently, I had never driven another 240 with ABS..."
In fact, my two '93s (with ABS, of course) have a pedal just as hard as any of my prior, non-ABS 240s, including the '84 I still have for comparison.

In any case, I can't imagine a normally working ABS system letting one rear wheel lock up without the fronts locking with it. That's definitely a sign that the system is faulty. And I don't believe it can happen just from fluid that's overdue for flushing, or even a bad caliper -- if the wheel was about to lockup, a proper working ABS system would detect this and reduce pressure to that caliper (or, actually, in the case of the older 3-channel system in our 240s, to both rear calipers).

I'm thinking that the ABS system is faulty, and maybe a previous owner just disabled it to hide the problem from prospective buyers. Is that possible? When you start the car (key in position III), does the ABS lamp light? It could have been removed, so it doesn't light up at all.

Good luck.