Final answer:
The breed of rabbit that produces high-quality wool without needing to be slaughtered is the Angora rabbit.
Step-by-step explanation:
The breed of rabbit that produces high-quality wool without needing to be slaughtered is the Angora rabbit. Angora rabbits have long, soft fur that can be sheared or plucked to harvest the wool. The wool from Angora rabbits is prized for its warmth and softness, making it ideal for making clothing and other textiles.