Humanoid motion trackers perform reliably within learned tracking distributions, but falls can move the robot into low-height, contact-rich states from which an advancing command is temporarily unreachable. Tracking-only policies may chase infeasible references, producing rapid, large-amplitude limb corrections that increase risk to the robot and its surroundings. We present StableMimic, a unified tracker trained beyond the nominal tracking distribution. Perturbed resets around multiple human get-up references expose prone, supine, off-balance, and intermediate ground-contact states, shaping structured recovery that returns the robot to the trackable region. Because tracking and recovery occupy markedly different state--action distributions, StableMimic uses dedicated experts for each regime and a proprioceptive gate that continuously blends their actions. A hidden successor-state objective teaches human-reference-shaped recovery without exposing reference identity or phase to the deployed Actor; deployment requires no get-up reference, recovery command, trajectory retrieval, or external policy switch. On the complete retargeted LAFAN1 dance subset, StableMimic achieves the lowest errors on all four tracking metrics among five methods. Across 100 matched push-to-fall trials per method, it recovers in 100/100 and attains the lowest values on six of seven post-fall motion and load measures, supporting improved interaction safety under this protocol. Real Unitree G1 dance and standing-reference deployments qualitatively demonstrate bounded limb motion, autonomous recovery, and command resumption.

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