Thanks to all for the replies. The suggestion that I should replace this cassette with the Sunrace cassette is something that I will pursue. Hopefully this will resolve the problem (if it fits correctly). I would be a little skeptical that the sprocket has broken off though, due to that the spacer, more than likely, would still be on the hub. I also believe that with such a failure would have been noticed while riding. Doing the calculations, the 13 tooth sprocket would have a large enough caliper diameter (root of tooth) to allow for clearance of the chain side-plates over the major diameter of the lock-nut. Thanks again for the advice!