Cloud-local LLM inference must keep sensitive user data on-device while exploiting cloud-grade reasoning, yet existing sanitization approaches (placeholder substitution, differential-privacy perturbation, and skill distillation) lack a release decision that is simultaneously safe and utility-preserving. We propose DR-SL (Dehydrate-Rehydrate with Self-Learning loop), which formalizes de-identification completeness as two measurable conditions: de-identification sufficiency under Pufferfish semantics, and task-information preservation via QA probes. A fully local two-branch verifier iterates dehydration under a lexicographic gate with guaranteed termination, backed by a deterministic hard line, an external strong-attacker re-test, and human fallback. We prove Fano-type lower bounds, a Pufferfish witness, and a rate-privacy feasibility criterion, and state their scope plainly: the bounds certify leakage, never safety, and are near-vacuous at our operating point, so release safety rests on empirical calibration, the hard line, and human review. On a worst-case fully task-coupled benchmark the loop reduces leakage from 0.457 to 0.304 (p approx. 0) and the release chain delivers 0.000 literal leakage at egress (160 instances, two strong attackers), the system degrading to certification-and-routing exactly as the feasibility criterion predicts. On a mixed-coupling benchmark the same safe point releases 67.5% of instances automatically at zero measured leakage, Pareto-dominating placeholder and selective-LDP corners under an identical release rule. Two human studies anchor the semantic utility metric (Spearman rho = 0.839) and the annotation gold (type-level recall at least 0.987). The exploratory self-learning hypothesis was not supported and is reported as such. All theoretical bounds pass numerical verification; code, synthetic datasets, protocol, and human-study packages are public.

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