KV-cache compression reduces LLM inference memory by evicting context tokens, but when the evicted tokens contain answer-bearing evidence, the model may hallucinate instead of recognizing that the compressed context is insufficient. We address this failure from a behavioral perspective: to our knowledge, this is the first work to formulate compression-aware abstention as a learning problem, in which a model learns to answer when supporting evidence survives compression and abstain when it does not. We construct supervision from compressor survival masks and tight answer-bearing spans, labeling examples as Confident when evidence survives and Abstain when it is removed. A 10.1M-parameter LoRA adapter trained on ~2.6K MuSiQue 2-hop QA examples reduces base-model hallucinations by 97% under prompt-style truncation while preserving correct answering on evidence-retaining examples. Unlike prompt-only abstention baselines, which over-abstain on many answerable high-retention examples, the trained adapter learns a conditional policy. We also evaluate the method under actual compressed-cache decoding, where multi-compressor training yields a 6-22x relative lift over the unaided base on evidence-retaining examples. Controlled-deletion experiments show that the learned behavior is driven by evidence content rather than input length alone.

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