Yes! Most rugs are constructed from a cotton foundation. Then, wool is strung around this foundation. Moths like to feed on the parts of the rug that are made of wool. This leaves the cotton foundation intact. You can always identify moth damage like this. Unfortunately, the process of repairing such accidents is much too complex to DIY. Rug moth damage repair requires an expert with years of experience. Luckily, the process is much cheaper than repairing an entire hole because the foundation doesn’t have to be rewoven from scratch on a loom.