The task of detecting moral values in text has significant implications in various fields, including natural language processing, social sciences, and ethical decision-making. Previously proposed supervised models often suffer from overfitting, leading to hyper-specialized moral classifiers that struggle to perform well on data from different domains. To address this issue, we introduce novel systems that leverage abstract concepts and common-sense knowledge acquired from Large Language Models and Natural Language Inference models during previous stages of training on multiple data sources. By doing so, we aim to develop versatile and robust methods for detecting moral values in real-world scenarios. Our approach uses the GPT 3.5 model as a zero-shot ready-made unsupervised multi-label classifier for moral values detection, eliminating the need for explicit training on labeled data. We compare it with a smaller NLI-based zero-shot model. The results show that the NLI approach achieves competitive results compared to the Davinci model. Furthermore, we conduct an in-depth investigation of the performance of supervised systems in the context of cross-domain multi-label moral value detection. This involves training supervised models on different domains to explore their effectiveness in handling data from different sources and comparing their performance with the unsupervised methods. Our contributions encompass a thorough analysis of both supervised and unsupervised methodologies for cross-domain value detection. We introduce the Davinci model as a state-of-the-art zero-shot unsupervised moral values classifier, pushing the boundaries of moral value detection without the need for explicit training on labeled data. Additionally, we perform a comparative evaluation of our approach with the supervised models, shedding light on their respective strengths and weaknesses.