Answer: Rose trees are usually grafted. It sounds like the root stock is sending up suckers. These will be more vigorous (and totally different from) than the grafted top and will overwhelm it, so they should be removed. Remove them right at the root as soon as they appear. It is also possible that the graft has failed. If the top of the tree has died completely so that there is no green wood left then I would, as you said, count this one out.
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