Have you ever noticed that large language models often struggle when attempting to modify their established fundamental facts? This paper examines the significant challenges that current knowledge editing techniques encounter when modifying information internally stored within models, particularly when dealing with highly interconnected knowledge. We find that existing methods typically operate at a superficial level, failing to adequately account for the complex networks of associations among different pieces of internal knowledge. This oversight frequently leads to unintended consequences, triggering a cascade of errors and inconsistencies, thereby severely undermining the model’s overall knowledge integrity. To better understand which types of knowledge can be effectively edited and which cannot, we propose a novel knowledge classification based on editability. Furthermore, we introduce the BoundaryEdit dataset, a new benchmark specifically designed for rigorously evaluating the performance of existing knowledge-editing techniques across different knowledge categories. Our experimental evaluation of mainstream knowledge-editing methods reveals significant limitations when attempting to modify fundamental, highly interconnected knowledge, often resulting in substantial breakdowns within the model’s knowledge system. To mitigate the risk of knowledge system collapse, we propose an automated classification approach leveraging advanced language models to distinguish editable from non-editable knowledge effectively. Our experiments using models such as ChatGPT-4o, Grok-3 beta, and Gemini 2.0 Flash demonstrate significant differences in accuracy across knowledge types, revealing distinct limitations particularly in handling partially information-missing and dependent uneditable knowledge.