I searched on some old threads and found it is caused by a fungus and is best prevented by spraying with a sulphur spray in spring before new growth.
In my case, I think several of the bareroot roses I bought in Feb. had a variety of dieback with cane canker. After blooming and being weakened by powdery mildew and blackspot, canker is finishing the job, although canker alone may have done so anyway eventually.
I also learned by reading an old thread, that you should disinfect the pruning shears after cutting back die back with black canes so as not to spread the fungus. That I didn't know. A bleach solution was suggested. I'm guessing that 70% rubbing alcohol would work just as good?
In the present case, this time it's Blue Moon that's succumbing. Even the bud union is black, but Dr. Huey looks like it's alive, peeking up through the soil.
This is a lesson to me that if I buy bareroot again, to avoid any with black spotches on the canes, or any with obvious die back that looks like canker.