Most cabinets have some particleboard in them. Some of it is obvious in shelving and jambs. Some has been covered by laminate or paint, but it's there. Nothing is wrong with particleboard. In some ways it is superior to plywood. It normally won't warp, and you can rip it or cross cut it without worrying about grain pattern. But particleboard does have its limitations. Edges break off, letting the shelving fall loose, and the pins on adjustable shelves get loose. You can fix them permanently by adding some screw cleats.
Open the door to the cabinet, and identify the shelf that has come loose. If the cabinet has adjustable shelves, simply remove the shelf. If its pinned in with nails, wiggle the shelf back and forth until it's loose enough to remove completely. If it still won't come out, pry behind it with a big screwdriver or pry bar until it releases.
Measure the two sides of the shelf. Cut two pieces of the 3/4 x 3/4 screw cleat material 1 inch shorter than the measurement. Drill 4 holes with a 3/16-inch bit spaced evenly down the length of both screw cleats. Turn the cleat 1/4 turn and drill 4 more holes at 90 degrees to the first set of holes.
Reach inside the cabinet, and remove any loose nails, wood chips, residual glue and old support pins. Scrape along the edge where the old shelf was with a putty knife to clean it. Clean up the debris in the bottom of the cabinet, and discard any old nails or screws.
Lay a bead of glue along the edge of the screw cleat; lay it glue-side down where you measured and screw it on. Glue both sides.
Measure inside the cabinet from the floor to the bottom line that was left when the shelf was removed. Cut 4 spacers 3/4 inch less than the measurement, and stand them up inside the cabinet to support the shelf when you screw it back in.
Slide the shelf back into the cabinet, and place it atop the 3/4 supports. Reach under with the screw gun, and screw it on using eight 1 1/2-inch screws.