There are a few things I've done in the past but this is how I'm handling the problem this time. I have a few 'kilt pins' and rolled up the excess rug and pinned thru all the layers on the outer margin of the rug. One pin on the left side.....
...and another pin on the right side. You can see the roll is still tight.
However, if it was a really long and heavier rug you could also take a length of yarn and thread through the middle of the rug and tie it up to prevent it from unrolling. I have also done that when the rug was a long runner.
Have heard of people placing a TV tray or other table in the back and placing the rug on that. But since I turn my frame that wouldn't be of any help for me.
Have a great evening.