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We study vulnerability persistence in LLM-generated software and introduce Feature--Security Table (FSTab) with two components. First, FSTab enables a black-box attack that predicts likely backend vulnerabilities from observable frontend features and knowledge of the source LLM, without access to the backend or source code. Second, FSTab provides a model-centric evaluation that quantifies how consistently a model reproduces the same vulnerabilities across programs, semantics-preserving rephrasings, and application domains. We evaluate FSTab on state-of-the-art code LLMs, including GPT-5.2, Claude-4.5 Opus, and Gemini-3 Pro, across diverse application domains. 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