A leaking pot means that the carpet under the pot gets wet and never dries completely. This wonderfully damp, dark, and warm environment breeds microrganisms that snack on the cotton warp and weft of the rug. The wool pile can be damaged as well, but the most extensive trouble occurs as the foundation of rugs with cotton warp and weft falls apart. After several months of conscientiously watering a plant with a leaking pot, you may pick up the pot and have a disk of deteriorated rug come with it! This can be an expensive development. The best repair is to reweave the hole. The weaver who originally constructed the rug made $5 or $6 per day; you'll be paying a skilled rug repair person $20+ (or maybe a lot more!) per hour for a repair that can take days to complete. To add insult to injury, you'll probably need to repair a water-damaged spot on the hardwood floor as well.
If you must put a potted plant on a rug, check that the pot is absolutely water tight, and be extremely careful not to over water the plant. Better still, use a pot stand to raise the pot up off the rug so you can see if there is a problem with a leaky pot. If you have a potted plant sitting on a rug, go check it right now!