Question

Cocoon type worm   Cocoon thing with live worm in it eating leaves. Attached to bottom of leaves

Answer
There are many types of insects that it can be, close to 100 types will do that.
What is important is why  it is attacking the rose in the first place and that is nutrition.
so
I have to ask you what are you feeding your roses?
If you are not doing so organically then yes you will have this problem more then if you were organic since organic relies of a broad range of nutrition then its chemical counter parts.

Use BT to control
Use a good organic rose fertilizer
avoid high nitrogen fertilizers


prune back and plant areas that have  and promote new growth.