Clean the rug. A rug that has been frayed and ripped through heavy use is probably due for a good cleaning. Vacuum the rug thoroughly. Dip a rag into upholstery cleaner. Dab at any stains with the rag, lifting the stain from the rug fibers. Rinse the rag with clean water. Continue dabbing at the spots with clean water until the stain and all cleaner are removed from the rug.
Insert a seam ripper under the thread that attaches the binding to the rug. Snap the threads to completely remove the binding. This is only necessary on the edge that is damaged.
Take the binding with you to a fabric store. Match the remnant with new binding. Make sure the pieces match in both size and color.
Lay the binding tape along the edge of the rug. Extend the binding tape 2 inches past the rug's edge. This will allow extra fabric for hemming. Cut the binding tape.
Iron the tape in half so that a sharp crease runs down the middle. Place the tape on the edge of the rug so that it matches the rest of the binding. Pin it in place with straight pins.
Attach the binding to the rug. Use the same stitch used on the rest of the rug. Fold the corners to match the other three corners and stitch those, as well.