Any damage to your rug should be addressed immediately: the longer something is left, the worse it is likely to get. Burns, cuts or fringe damage will cause the rug to deteriorate quickly.
To state the blindingly obvious: the most important thing with repairs is to use someone who knows what they are doing. Find a professional rug repairer. A rug that has been professionally repaired should look as good as new.
Tears or cuts in a handmade rug can often be repaired by joining the knots together from the back of the carpet. Silk thread is often the bet medium as it is stronger and finer than wool or cotton.
Rug Out of Square or Wrinkled
If a rug is out of square or has built-in wrinkles, sizing or blocking may help.