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Zero-shot multi-label text classification (ZMTC) requires models to predict multiple labels for a document, including labels unseen during training. Previous work assumes that models leveraging label descriptions ensures zero-shot capability. However, we find that supervised methods, despite achieving strong overall performance, lose their zero-shot capability during training, revealing a trade-off between overall and zero-shot performance. To address the issue, we propose OF-DE and OF-LAN, which preserve the zero-shot capabilities of powerful dual encoder and label-wise attention network architectures by freezing the label encoder. Additionally, we introduce a self-supervised auxiliary loss to further improve zero-shot performance. Experiments demonstrate that our approach significantly improves zero-shot performance of supervised methods while maintaining strong overall accuracy.