Standard accounts of scientific inquiry treat failure as eliminative—false conjectures are discarded, and progress consists in the selective retention of survivors. I argue that this characterization is incomplete. Under conditions of epistemic indeterminacy, where the space of live possibilities is not fully specified in advance, failure may possess positive epistemic value beyond mere elimination. To capture this, I propose a Generative Failure Criterion for epistemic appraisal: the epistemic value of an idea is partly determined by the degree to which its failure yields diagnostic constraints that restructure the space of live possibilities for subsequent inquiry. I distinguish between sterile and generative forms of failure and identify two structurally distinct modes of epistemic productivity. First, intra-domain restructuring, in which breakdown exposes hidden constraints, clarifies assumptions, or reorganizes the internal architecture of a field. Second, inter-domain reinterpretation, in which a failed or apparently irrelevant proposal acquires significance within a different evaluative context. These modes are illustrated through historical cases from physics and materials science. The paper addresses objections from underdetermination, retrospectivity, and reducibility to existing frameworks, and concludes that epistemic appraisal in temporally extended inquiry must attend not only to confirmation and survival but also to the generative transformation of possibility itself.