Entity structure extraction, which aims to extract entities and their associated attribute–value structures from text, is an essential task for text understanding and knowledge graph construction. Existing methods based on large language models (LLMs) typically rely heavily on predefined entity attribute schemas or annotated datasets, often leading to incomplete extraction results. To address these challenges, we introduce ZOES, a novel approach to entity structure extraction that does not require any schema or annotated samples. ZOES operates via a principled mechanism of enrichment, refinement, and unification, based on the insight that an entity and its associated structure are mutually reinforcing. Experiments demonstrate that ZOES consistently enhances LLMs’ ability to extract more complete entity structures across three different domains, showcasing both the effectiveness and generalizability of the method. These findings suggest that such an enrichment, refinement, and unification mechanism may serve as a principled approach to improving the quality of LLM-based entity structure discovery in various scenarios.