Although the LiDAR SLAM technique has been already widely deployed on various robots, it may still suffers from degeneracy caused by inadequate constraints in scenes with sparse geometric features. If the degeneracy is not detected and properly processed, the accuracy of localization and mapping will significantly decrease. In this letter, we propose the P2d-DO method, which consists of a point-to-distribution degeneracy detection algorithm and a point cloud-weighted degeneracy optimization algorithm, to relieve the negative impact of degeneracy. The degeneracy detection algorithm outputs factors that characterize the degeneracy state by observing changes in the distribution probabilities within a local region. Factors reflecting the confidence of the point clouds are then fed to the degeneracy optimization algorithm, enabling the system to prioritize reliable point clouds by assigning larger weights during the matching process. Comprehensive experiments validate the effectiveness of our method, demonstrating significant improvements in both degeneracy detection and pose estimation in terms of accuracy and robustness.