Researchers have introduced Hybrid-Policy Self-Editing (HPSE), a novel framework designed to address the lack of "composability" in Unstructured Knowledge Editing (UKE). While current editors can inject free-form passages into Large Language Models (LLMs), the models often fail to perform atomic fact retrieval or multi-hop reasoning based on that new information. The authors identify this failure as a result of editors relying passively on the injected passage rather than actively integrating it. To solve this, HPSE treats editing as a proactive self-distillation process where the model learns from a privileged in-context state without requiring external supervision. Because the injected knowledge is novel, the model's standard on-policy rollouts often fail to cover the new facts, making pure on-policy distillation ineffective. HPSE overcomes this by utilizing a hybrid rollout strategy that strategically inserts missing facts into the student model's trajectory exactly where its coverage is insufficient, while maintaining on-policy behavior elsewhere. Theoretical analysis and empirical testing across four LLM backbones and two existing KE editors demonstrate that HPSE provides plug-and-play improvements, enabling models to better compose and reason with unstructured, newly injected knowledge.