This has been addressed, actually - in 'Batgirl Year One', Babs, having made her decision to pursue a life of crimefighting, plans on getting in some roof-swinging practice. She goes up onto the roof of a skyscraper, lassoos a nearby gargoyle, and dives off the roof, rope in hand - only to be snatched out of the air by Batman and Robin, who have been watching her. She's wildly indignant at first, until Batman explains that he just saved her life - she was using plain ol' normal rope, which, as you pointed out, would have ripped her arm from her shoulder when she got to the limit of it. The Batclan, it turns out, use a special kind of rope that has stretch and give to it, so that when its limit is reached, it doesn't just twang taut like a fiddlestring - it stretches a bit, like a bungee cord, which allows the swing-ee to complete the apex of their swing without getting ripped apart. I'm not sure just how scientifically accurate this is, but it sounds all right to me - after all, there are bungee jumpers and cliff jumpers and so forth who manage similar feats without getting torn to shreds.