I found a nice photo on the Huntington Gardens website, which I will post below.

You will see that it just ends in leaves, with no hint of any rose bud forming.

What to do is cut the blind shoot shorter, so that it can make a side branch out on one side and, hopefully, make some flowers.

Here is a link that might be useful: blind shoot photo

I've always figured the rose needed those leaves and/or wood to create and store food with/in and didn't worry about them. The foliage creates food and shades the structure from sun scald, so I just let them do that and didn't worry about them. When I do any pruning or clean up, I might cut them back, but not always. Kim

Your way makes sense, Kim.

Wretched little things with their dead corn silk ends!!
My garden seems to get a great many of them, and they are ever so frustrating. Just about the time you get all jazzed and hopeful about new growth, you realize that nothing is ever going to come of it. I've seen the theory put forth that roses make them more frequently at times when there have been great fluctuations in temperature. Anyone care to weigh in on that theory?
I also find that some of my roses make them on brand new side shoots virtually right at the main cane, so it's not really possible to cut them back to sprout again. There's nothing for it but to remove it in its entirety and hope to be graced with a new branch elsewhere.
The white rose Full Sail had a particular talent for this, which is one reason why it Sleeps with the Shovels. Anyone else find that particular roses are especially prone to kicking out blind shoots?

Kay