Search Engines Never Say No: How Frozen Agents React When the Retrieval Tool Refuses

Abstract

A search tool never says no: it returns its top-k passages even when the index holds no answer, so the agent sees irrelevant text instead of a miss signal. We ask what frozen search agents do when the tool refuses instead. On an index-hole testbed (257 NQ and 300 HotpotQA questions run with and without their gold passages in a 21M-passage BM25 index), seven agents receive one of five refusal wordings. An un-announced one-sentence refusal raises abstention on unanswerable questions from 23% to 97% on average for Qwen3-8B/32B and from 28% to 57% for Claude Haiku 4.5, cutting wrong answers almost one-for-one and beating a system-prompt instruction by 51 points on average. Search-R1 ignores the refusal and fabricates retrievals; Claude Sonnet 5.5 and Opus 5.5 answer from memory (abstention +2 points) and obey a system-prompt directive instead (+16). We also found that wording matters: an explanation beats a bare token; a directive inside the observation is decisive for Haiku; a soft warning is useless. Realistic triggers, from a lightweight score-based predictor to an LLM grounding judge, fall well short of the oracle, and all land on a benefit-versus-signal-quality curve that prices any trigger by its recall at a fixed false-refusal budget: for compliant agents the bottleneck is the detector inside the tool, not the agent, and the curve tells future detector work what each point of recall is worth.