Cross-domain retrieval (CDR), as a crucial tool for numerous technologies, is finding increasingly broad applications. However, existing efforts face several major issues, with the most critical being the need for accurate supervision, which often demands costly resources and efforts. Cutting-edge studies focus on achieving unsupervised CDR but typically assume that the category spaces across domains are identical, an assumption that is often unrealistic in real-world scenarios. This is because only through dedicated and comprehensive analysis can the category spaces of different domains be confirmed as identical, which contradicts the premise of unsupervised scenarios. Therefore, in this work, we introduce the problem of Universal Unsupervised Cross-Domain Retrieval (U^2CDR) for the first time and design a two-stage semantic feature learning framework to address it. In the first stage, a cross-domain unified prototypical structure is established under the guidance of an instance-prototype-mixed contrastive loss and a semantic-enhanced loss, to counteract category space differences. In the second stage, through a modified adversarial training mechanism, we ensure minimal changes for the established prototypical structure during domain alignment, enabling more accurate nearest-neighbor searching. Extensive experiments across multiple datasets and scenarios, including closet, partial, and open-set CDR, demonstrate that our approach significantly outperforms existing state-of-the-art CDR works and some potentially effective studies from other topics in solving U^2CDR challenges.