Deploying humanoid task policies requires reliable runtime monitors that anticipate unrecoverable falls in time to trigger a fallback. We formulate this task as learning the stochastic, finite-horizon recoverability envelope of a given fallback policy. Synthesizing this monitor is challenging: existing methods assume training data naturally covers the recoverability envelope, yet acquiring such data remains a major bottleneck for contact-rich systems. Consequently, they recover only a fraction of the true envelope, leaving them prone to optimistic hallucinations for out-of-distribution (OOD) inputs. We resolve this via a unified framework that iterates between value learning and active exploration. Data exploration is reframed as a reach-avoid problem, where an uncertainty-guided explorer systematically uncovers unseen states while avoiding confidently unrecoverable regions. This loop is further supported by a combined Temporal Difference and Monte Carlo objective for accurate in-distribution value prediction and reliable uncertainty estimation. By explicitly treating the remaining high-uncertainty regions as unrecoverable, the monitor mitigates optimistic OOD hallucinations. Evaluated on stochastic benchmarks and a 29-DoF Unitree G1 humanoid, our approach drastically improves monitor coverage and accuracy and successfully transfers zero-shot to real-world hardware.

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