To repair a loose thread in a braided rug, take the thread out, and connect the two parts of the rug, using a rounded upholstery needle. If there is a problem with a larger part of the rug, undo it up to the place where the problem is, and braid the rug again. Be sure to add more material accordingly, as there isn't going to be enough. Replace the coil on the rug, starting to sew from the bottom.
If you need to repair a different type of an area rug, connect the edges of the tear, and sew them together on the inner side of the rug. For this task, it is best to use a rounded upholstery needle and strong thread that is the same with the color of the rug. If the tear is too large and can't be repaired by sewing, use fibers from another part of the rug to cover the tear. Take the replacement fibers out of a part of the rug that is not visible, place them onto the area of the tear by using a toothpick, and fix them in place with glue.
If the rug is torn and a repair is needed right away, there is a chance that all the fibers remained in place. In this case, clean the edges of the tear of dust and loose fibers, coat one edge with glue, and connect the sides together. Rub the area with a nail brush after the glue dries to get a more natural look.