Little was known about rug when I set out to repair it. I tested a few strips of the fibers to learn more about how to proceed. This "burn test" told me the fibers were a mix of cotton batting, polyester, and wool.
I trimmed the unsalvageable edge, removed a few loops to expose enough backing to fold under and secure the new edge. This meant losing a half-inch at one end of the rug. The holes in the center were reinforced with new linen backing that was sewn in place and hooked with materials saved from the end and a few strips I had on hand.