Answer: Your roses probably sprouted from their rootstocks. Roses, like many other plants, including fruit trees, are often grafted. That is, the upper part (in your case, the hybrid tea) is grafted onto another rootstock, often a wild relative that is particularly hardy or disease resistant. So what you saw were sprouts coming from that rootstock and overtaking the less vigorous hybrid tea. On grafted plants it is important to prune off any of these root suckers to prevent this problem.
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