They are attached to the corners to keep fitted sheets from sliding out of place. The sheet is placed over a button-like fitting, then a wire clip (kind of hourglass shaped) is pressed over that and slid into position to secure the sheet at that point.
WY, YOU NAILED IT! Exactly what I was seeking. Thank you, and have a wonderful weekend.





















































I think they are usually just called sheet holders, or they can be called sheet suspenders. Check out this page from Amazon, and be sure to scroll down to where similar products are offered. There are a few variations in the design of the basic product.
http://www.amazon.com/Sheet-Suspender-sheets-smooth-tight/dp/B0014AMBWK
Sheet Grippers, Garters, Straps, Suspenders. Available in the bedding aisle everywhere, and e-bay is lousy with them. Slight pain to attach at each bed change, but worth it. They really work!