Many bed-owners ought to get one of this, the Sealy Mattress Gripper:

Stop fussing with that shifty mattress while changing the sheets. These non-slip strips lay flat between the boxspring and mattress to keep your mattress in place. Grippers won’t mold or mildew and they rinse clean with soapy water. Sold in sets of two, each strip measures 12 1/2″ W x 70″ L

Product is sold at Bed Bath & Beyond