I have the impression that 折らで would be 折らないで without ない. If that's the case is it an artistic choice or some obscure grammar?
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In classical Japanese, で after an irrealis-form (未然形) means ないで in modern Japanese. So 折らで means 折らないで or "without snapping off".
This で is surviving as part of ならでは (etymologically, copula-なり + で + contrastive-は → "unless so", "if it were not" → "unique to", "found only in")