The elastic on your fitted sheets, including king size, can become stretched and the sheet will fit loosely. Sleepers with restless-leg syndrome may pull even well-fitted sheets loose at night. Sometimes, mattress pads may make the mattress too thick and the corners don't fit down over the corners well. Here are some simple solutions to this problem.
The simplest way to make your bedsheet corners more secure is with commercial sheet grippers. Hospital supply outlets and some linen stores sell sets of these elastic corner bands. They have end fasteners similar to those on old-fashioned women's garters or plastic clips. The garters clips attach 8 or 10 inches from the corners and fasten diagonally across the corner to hold the sheet under the mattress. Properly fastened, the elastic bands will pull the sheets tight over the corners. The sheet grippers come with instructions.
If you are handy with a sewing machine, you can sew new elastic over the old. Buy a band of elastic of suitable length and lay it over the top of the old elastic. Stretch the new elastic as you sew it around the outside edges. Once it's sewn in place, it will bunch up the old corner making it tighter.
Use an old or cheap pair of suspenders to keep the sheet tight. Attach each clip to a corner of the sheet under the mattress, pulling it tight to form an "X." The pressure on the corners keeps the sheet from shifting on the bed.