Take an old dresser and remove the drawers. You can keep the top drawer in place for storage. Remove sides and backs of drawers. Next, take the bottoms off. Measure the opening and then take two of the drawer bottoms and use as backing reinforcement to the drawer fronts as shown in the photo above. Attach a rope or string to the dresser shell and the drop door. Now cut a small rectangular opening on the side your cat will be accessing the hideaway box. Cover (from the inside) the opening with cloth or thin plastic sheet.
You will now have a DIY hideaway cat litter box.