Jerry, the couple of times I've dealt with this the roller stayed in place after the plastic broke. It is my (admittedly vague) recollection that the plastic piece was there more for assistance in assembly? Could definitely be mistaken there as it's been years since I had reason to deal with that issue and even then it wasn't a pressing problem. The roller did stay in place after breakage of the plastic though. Twice in my experience. That much I am sure of.
I think you're right Don, the little strap is probably superfluous once the two bushings attached to it are installed on the roller and inserted into the lever. That photo that was posted wasn't clear enough to be able to tell if the piece over to the right was one of the bushings or not, but if the bushing is broken or missing it would be a very good idea to replace the bushings and roller soon, IMHO.
Jerry