Agents that answer questions from compressed or retrieved memory must recognize when the evidence a query needs is no longer in memory. Benchmarks for this task usually create insufficient-evidence examples by deleting supporting passages. We show that this construction leaks the label through memory size: on MuSiQue, a classifier that only counts paragraphs reaches an area under the ROC curve (AUROC) of $0.979$ for detecting unsafe memory, higher than the lexical estimator we initially evaluated. We propose a size-matched construction that provably removes this shortcut, and use it to study MemSafe, an estimator that cross-encodes the query with each memory unit and aggregates the units with a set transformer. Across three multi-hop question answering datasets and five seeds, MemSafe reaches $0.968$ and $0.983$ AUROC on MuSiQue and HotpotQA, $0.26$ to $0.39$ above a lexical baseline, while the third dataset, 2WikiMultiHopQA, is saturated. A frozen pretrained cross-encoder with a logistic head already closes $41\%$ of the MuSiQue gap between the lexical baseline and MemSafe. At the same time, MemSafe degrades more than a weak baseline on the unanswerable questions released with MuSiQue, reaches only $0.639$ AUROC on SQuAD~2.0, and needs several thousand clinical training examples before it outperforms a feature-based estimator. Used as a gate for a 7B reader, it reduces the error rate on answered questions from $0.850$ to $0.631$ at $5\%$ coverage, outperforming both reader confidence and, on average, the ground-truth integrity label, although a 7B LLM judge is the better gate at $10\%$ coverage. These results indicate that the way insufficient evidence is constructed matters as much as the estimator that detects it.

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