I had an '81 Mini that had that...and will NEVER forget the night I tried putting it back together in the dark in the wee hours with three tired and cranky friends waiting in the car. I was a young G.I. in Germany and we'd just left the bar after it closed. I'd parked in a place that I really shouldn't have and had to drop off a 4" kerb to exit it. The edge caught on the front silencer and caused the pipe to be yanked off the manifold, breaking away all of the flange on the pipe except for one bit about 1/2" wide. I figured I could get it to hang on that until we got back to base if I was gentle with it. But after 30 minutes of blind fettling there was no joy, so I went round back of the car, grabbed hold of the tailpipe, put a foot into the bumper, and gave it a mighty pull and twist and was free of the whole thing which I tossed into an alley and left there.
Minis were rare in Germany at that time ('88) but I found one in a local scrapyard that had an intact exhaust-system, and it was nicer/sportier than the one I abandoned! Made a nice raspy note. Too bad the car itself didn't last much longer than that, but that's another story for another time.