The cracked or torn binding will need to be stabilized first so that it does not keep running through the length of your rug. Do this by matching up some heavy gauge sewing thread to a basic color of your rug. This thread is available at any department store in the sewing section.
If the tear in the binding is exposed on the top of the rug, now is the time to trim some fibers from a corner and press them into the separation. This will cover up any binding spots that might have been showing, and the stitching will hold them in place.
Flip over the area rug and expose the binding separation; this is where you will begin. Manually thread a needle with your choice of colored thread, and beginning at one end of the tear, begin stitching the tear closed. The color of your thread will make it difficult, if not impossible, to see this repair, so stitch your way carefully from one side to the other.