Current methods for document key information extraction (DKIE) rely heavily on labeled data with high annotation costs. To mitigate this issue, the semi-supervised learning (SSL) paradigm, which utilizes unlabeled document samples, has gained broad attention in DKIE. However, existing SSL methods require labeled and unlabeled data to share an identical label space, which is impractical in many DKIE tasks (i.e., some unlabeled samples do not belong to any known classes in the labeled set). In this paper, we formulate this problem as Class-Missing Semi-supervised (CMSS) DKIE. In DKIE, unknown classes usually belong to minority and fine-grained categories, intensifying the misconnections between known and unknown classes and making CMSS more challenging. To address this issue, we propose Synergistic Refinement Estimation (SRE), a progressive prototype estimation scheme that alleviates the unknown classes bias to the majority known classes on long-tailed unlabeled data. Furthermore, dynamic threshold hash rectification and structural calibration mechanisms are proposed to correct connections between fine-grained classes. Extensive experimental results demonstrate that SRE surpasses existing state-of-the-art methods on several DKIE benchmarks. Code is available at https://github.com/anonymoulink/SRE_DKIE.