The ones that will truly not roll or fold over are the ones that have the boning feature in the rear of the girdle. This is metal rods of a few inches long that are inserted into a little pocket of the fabric to give your back the support it needs. These added pieces will prevent the fabric from rolling or bending over. The ones that do not have this quality will probably bend or roll depending on how much you use them and how far you bend. The body shape also has a lot to do with this happening too. For those women who generally have a larger top than the bottom, this could be a regular problem.