Providing subject access to information resources is an essential function of any library management system. Large language models (LLMs) have been widely used in classification and summarization tasks, but their capability to perform subject analysis is underexplored. Multi-label classification with traditional machine learning (ML) models has been used for subject analysis but struggles with unseen cases. LLMs offer an alternative but often over-generate and hallucinate. Therefore, we propose a hybrid framework that integrates embedding-based ML models with LLMs. This approach uses ML models to (1) predict the optimal number of LCSH labels to guide LLM predictions and (2) post-edit the predicted terms with actual LCSH terms to mitigate hallucinations. We experimented with LLMs and the hybrid framework to predict the subject terms of books using the Library of Congress Subject Headings (LCSH). Experiment results show that providing initial predictions to guide LLM generations and imposing post-edits result in more controlled and vocabulary-aligned outputs.