Recent years have witnessed an explosion of Multi- view Subspace Classification (MSCla) and Multi-view Subspace Clustering (MSClu) methods for various applications. However, their theoretical foundation have not been well explored and understood. In this paper, we investigate the multi-view subspace-preserving recovery theory, which is the theoretical underpinnings for MSCla and MSClu methods. Specifically, we derive novel geometrically interpretable conditions for the success of multi-view subspace-preserving recovery. Compared with prior related works, we make the following innovations: First, our theory does not require the equality constraint, which is a common requirement in prior theoretical works and may be too restrictive in reality. Second, we provide both Individual Theoretical Guarantee (ITG) and Universal Theoretical Guarantee (UTG) for multi-view subspace-preserving recovery while prior works only give the UTG. Third, we also apply the proposed theory to establish theoretical guarantees for MSCla and MSClu, respectively. Numerical results validate the proposed theory for multi-view subspace-preserving recovery.