The rapid integration of Generative AI (GenAI) and Large Language Models (LLMs) in sectors such as education and healthcare have marked a significant advancement in technology. However, this growth has also led to a largely unexplored aspect: their security vulnerabilities. As the ecosystem that includes both offline and online models, various tools, browser plugins, and third-party applications continues to expand, it significantly widens the attack surface, thereby escalating the potential for security breaches. These expansions in the 6G and beyond landscape provide new avenues for adversaries to manipulate LLMs for malicious purposes. We focus on the security aspects of LLMs from the viewpoint of potential adversaries. We aim to dissect their objectives and methodologies, providing an in-depth analysis of known security weaknesses. This will include the development of a comprehensive threat taxonomy, categorizing various adversary behaviors. Also, our research will concentrate on how LLMs can be integrated into cybersecurity efforts by defense teams, also known as blue teams. We will explore the potential synergy between LLMs and blockchain technology, and how this combination could lead to the development of next-generation, fully autonomous security solutions. This approach aims to establish a unified cybersecurity strategy across the entire computing continuum, enhancing overall digital security infrastructure.