Many recent approaches for vulnerability detection use large language models (LLMs) to classify functions as vulnerable or benign, leaving developers to locate the exploitable statements. Furthermore, while these approaches have shown performance improvements, they still fall short in distinguishing vulnerable from patched real-world functions. This paper presents SBVul, an agentic approach that detects exploitable statements in C/C++ functions. In Phase~1, an LLM agent explores the function and its repository and identifies candidate statements. In Phase~2, a second agent analyzes the control and data flow of each candidate and confirms it, rules it out, or marks it uncertain. We created a manually verified ground truth of exploitable statements for 200 pairs of the PrimeVul Paired test set and ran SBVul with the open-weight models Qwen 3.8 and DeepSeek V4.1 Flash and Anthropic's Sonnet 5.5 and Opus 5.5. Phase~1 identifies ground-truth statements in 56--77% of the vulnerable functions, and Phase~2 confirms such a statement with an explanation accepted by an LLM judge in 26--73%. However, all models also confirm candidates in 23--61% of the patched functions. Across vulnerable and patched functions, the highest statement-level precision is 0.315 at a recall of 0.605 obtained with Opus 5.5 (xhigh). At the function level, SBVul with Opus 5.5 classifies 42.0% of the pairs correctly, compared with 33.8% reported for the best previous approach.

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