The software supply chain has become an increasingly exposed attack surface because of its reliance on intricate yet fragile dependencies. Existing defenses such as GitHub Dependabot often raise many false alerts because their coarse-grained matching cannot determine whether a vulnerable dependency is actually exploitable. Security analysts typically spend substantial time assessing vulnerability exploitability case by case. Recent LLM agents have emerged as promising candidates for this task given their advanced capabilities in coding and cybersecurity, yet no existing benchmark evaluates them on it. Prior benchmarks target zero-day settings, where agents detect and exploit previously unknown vulnerabilities. In contrast, software supply chain security focuses on how known vulnerabilities in upstream dependencies affect downstream projects. This requires agents to reason across repositories and determine whether an upstream vulnerability is exploitable in the downstream project. To address this gap, we introduce VEX-Bench, the first benchmark for evaluating LLM agents' ability to assess the exploitability of software supply chain vulnerabilities. It contains 75 real-world cases mined from GitHub and labeled by security experts, covering Python, Java, and Go. We evaluate nine models across three agent harnesses. While GPT-5.5 and Claude Opus 4.6 reach approximately 80% F1 on binary vulnerability-status classification, only GPT-5.5 surpasses 70% macro-F1 on fine-grained justification classification. This gap highlights the challenge of moving beyond binary exploitability assessment to identifying fine-grained exploitability reasons. Code and data: https://github.com/steven1518/vex-bench

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