Those things hanging down, kids, are garters (in Britain, suspenders.) They held up the stockings. Some of you may never have seen stockings either. They were replaced by pantyhose, which might have had something to do with the demise of the girdle, come to think of it.
Pantyhose themselves may be on the way out these days. Far as I can see, it's bare-legged in the summer now, and tights in the winter. The world marches on, leaving girdles and stockings back in the Dark Ages. But if you search on eBay under its classy word for "old" and "used", you'll find that people are actually bidding on and buying "vintage girdles". Maybe it's collectors -- remember the beginning of "Cold Comfort Farm"?
Today I see ads for an exciting new invention that sure looks like what we knew as the panty girdle, except that it is disguised with a super-cute name, something along the order of Spanky? Spunky? or maybe just Silly. I predict failure for this undertaking. We’ve come a long way, baby, and I don't see us going back.