i believe the term Sautoir may come from "Saltire" which is a diagonal cross as seen on a flag.

yes there do exist diagonally worn long loops of beads in various traditions... think of Miss World in her sash... or the leather bandoliers with rows of bullets...

i notice "Sautoir" in some online dictionaries is not so specifically a single diagonal strand- however i prefer only to use the term to clearly distinguish a diagonally worn long necklace, and i describe other long necklaces as either a long continuous loop, a pendant necklace, a tassel necklace or a Liberty necklace, or the style that ties 2 ends together as a lariat style.

its hard to imagine those in favour of women's suffrage wearing anything so long in the 1900s because you can't do much housework if your jewellery is so long that it will catch on the furniture...!