Can't say about the rose, other than leave it there and wait and see. But I hope it wasn't a grafted rose, because in that case the roots won't produce the same rose as the canes.

What you can do, though, is describe the rose and see if we can identify it, maybe it will turn out to be replaceable.

The bud where the rose was grafted may look dead and yet a new cane may yet break from the bud, wait and see. If growth starts from under the bud it will be rootstock, and if allowed to grow will take any energy that might cause a break from the bud, and I would remove any such growth. Al