This study investigates unsupervised anomaly action recognition, which identifies video-level abnormal-human-behavior events in an unsupervised manner without abnormal samples, and simultaneously addresses three limitations in the conventional skeleton-based approaches: target domain-dependent DNN training, robustness against skeleton errors, and a lack of normal samples. We present a unified, user prompt-guided zero-shot learning framework using a target domain-independent skeleton feature extractor, which is pretrained on a large-scale action recognition dataset. Particularly, during the training phase using normal samples, the method models the distribution of skeleton features of the normal actions while freezing the weights of the DNNs and estimates the anomaly score using this distribution in the inference phase. Additionally, to increase robustness against skeleton errors, we introduce a DNN architecture inspired by a point cloud deep learning paradigm, which sparsely propagates the features between joints. Furthermore, to prevent the unobserved normal actions from being misidentified as abnormal actions, we incorporate a similarity score between the user prompt embeddings and skeleton features aligned in the common space into the anomaly score, which indirectly supplements normal actions. On two publicly available datasets, we conduct experiments to test the effectiveness of the proposed method with respect to abovementioned limitations.