Non-rigid alignment of point clouds is crucial for scene understanding, reconstruction, and various computer vision and robotics tasks. Recent advancements in implicit deformation networks for non-rigid registration have significantly reduced the reliance on large amounts of annotated training data. However, existing state-of-the-art methods still face challenges in handling occlusion scenarios. To address this issue, this paper introduces an innovative unsupervised method called Occlusion-Aware Registration (OAR) for non-rigidly aligning point clouds. The key innovation of our method lies in the utilization of the adaptive correntropy function as a localized similarity measure, enabling us to treat individual points distinctly. In contrast to previous approaches that solely minimize overall deviations between two shapes, we combine unsupervised implicit neural representations with the maximum correntropy criterion to optimize the deformation of unoccluded regions. This effectively avoids collapsed, tearing, and other physically implausible results. Moreover, we present a theoretical analysis and establish the relationship between the maximum correntropy criterion and the commonly used Chamfer distance, highlighting that the correntropy-induced metric can be served as a more universal measure for point cloud analysis. Additionally, we introducelocally linear reconstruction to ensure that regions lacking correspondences between shapes still undergo physically natural deformations. Our method achieves superior or competitive performance compared to existing approaches, particularly when dealing with occluded geometries. We also demonstrate the versatility of our method in challenging tasks such as large deformations, shape interpolation, and shape completion under occlusion disturbances.