Decentralized training of large language models has emerged as an effective way to democratize this technology. However, the potential threats associated with this approach have not been carefully discussed, which would hinder the development of decentralized training infrastructures. This paper aims to initiate discussion towards this end by exploring the robustness of decentralized training from three main perspectives. First, we demonstrate the vulnerabilities inherent in decentralized training frameworks in terms of hardware, data, and models. Second, we highlight the fundamental difference between decentralized foundation model training and vanilla federated learning, where the security techniques employed in federated learning cannot be applied directly. Third, we discuss the essential components required for a robust and efficient decentralized training framework and present a case study by modeling a concrete threat model. Our objective in this vision paper is to emphasize the importance of addressing security concerns in the context of decentralized training for large language models.