Structural, not decorative
Warp threads run the length of the rug from end to end. Knots are tied onto them and weft threads pass between the rows to lock everything in place. Where the weaving stops, the warp continues and emerges as the fringe. Cut it short and you are cutting the structure the rug is built on. On machine-made rugs the fringe is usually sewn on afterwards and genuinely is decorative, which is where the confusion comes from.