In this paper, I expand upon the terminology surrounding David Lawton's concept of "double cycle" -- a recurrent tonal structure that suggests a parallel between two parts of a narrative. "Global double cycle," as I call it, is a parallel between the structure of the first acts and that of the opera as a whole. An initial structure that grows to embody the entire composition serves as an eloquent representation of fate, which Heraclitus defined as the necessary conclusion brought about by a person's character. Consequently, nineteenth-century operas dealing with fate sometimes feature a character-building phase (the opening acts) that structurally mirrors the culmination (the work as a whole). "Damaged-global double cycle" is my proposed term for a cycle with a marked flaw, serving as a representation of averted fate. As a case study in applying these new terms, I illustrate their presence in two nineteenth-century operas that deal with fate: Les Troyens by Hector Berlioz, and La Esmeralda by Louise Bertin.