Supply chain crisis prediction is a crucial task in business operations and risk management. However, existing research mainly focuses on identifying risk signals or predicting specific aspects of the supply chain, with relatively little emphasis on comprehensive crisis prediction. This challenge is further exacerbated by the scarcity of existing datasets. Moreover, when analyzing social media data, existing methods face challenges of noise and context specificity, affecting the accuracy of the prediction. To address these challenges, we propose SocioSupplyAlert (SSA), an innovative supply chain crisis prediction framework and create three domain-specific datasets based on X (formerly known as Twitter). SSA employs large language models (LLMs) for dynamic topic extraction and updating, enabling the precise identification of key topics that trigger supply chain crises. Furthermore, SSA utilizes LLMs for multidimensional topic classification and sentiment analysis of tweets, incorporating news data for crisis labeling. By leveraging a Voting Classifier to integrate multiple traditional machine learning and deep learning models, SSA can effectively predict the probability of supply chain crises. Experimental results on the datasets demonstrate that SSA outperforms baseline models, showcasing its outstanding generalizability and broad applicability. The dataset and code will be released upon paper acceptance.