We investigate the entity alignment (EA) problem with unlabeled dangling cases, meaning that partial entities have no counterparts in the other knowledge graph (KG), and this type of entity remains unlabeled. To address this challenge, we propose the framework \textit{Lambda} for dangling detection and then entity alignment. Lambda features a GNN-based encoder called KEESA with spectral contrastive learning for EA and a positive-unlabeled learning algorithm for dangling detection called iPULE. iPULE offers theoretical guarantees of unbiasedness, uniform deviation bounds, and convergence. Experimental results demonstrate that each component contributes to overall performances that are superior to baselines, even when baselines additionally exploit 30\% of dangling entities labeled for training.