Large Language Models are increasingly being applied for automated unit test generation in software engineering. This paper presents a comprehensive empirical study evaluating the effectiveness of LLM-generated tests under program code evolution. Through a mutation-driven framework analyzing 22,374 program variants and 8 different LLMs, the researchers assess how generated tests respond to semantic-altering and semantic-preserving changes. The study reveals that while LLMs achieve strong baseline performance with 79% line coverage and 76% branch coverage on original programs, test quality degrades significantly during software evolution. This work provides critical insights into the limitations of current LLM-based testing approaches and highlights the need for more robust test generation methods that can adapt to code changes.