The Hamming Quasi-Cyclic (HQC) cryptosystem is a prominent candidate in post-quantum cryptography, leveraging the hardness of decoding quasi-cyclic codes to ensure security against quantum adversaries. Despite its robustness, the security of HQC can be compromised by the presence of weak keys—keys that, due to structural anomalies or insufficient randomness, significantly reduce the cryptosystem’s resistance to attacks. This research presents a comprehensive analysis of weak keys within the HQC framework, emphasizing their role in enabling decryption failure attacks. We investigate how deviations in key properties, such as abnormal Hamming weights, patterned bit sequences, and improper quasi-cyclic structures, can lead to increased decryption failure rates (DFR). Through a combination of theoretical analysis and experimental validation, we demonstrate how these weak keys can be exploited to facilitate key recovery via decryption failures. Our study also explores the impact of weak keys on Information Set Decoding (ISD) attacks, revealing how structural weaknesses in the keys can dramatically reduce the complexity of such attacks. To mitigate these vulnerabilities, we propose a set of detection and prevention strategies aimed at ensuring the generation of strong keys in HQC. These include rigorous Hamming weight checks, enhanced randomness validation, and structural pattern detection during key generation. Our findings underscore the critical importance of robust key management in maintaining the security of HQC and similar post-quantum cryptosystems. This research contributes to the broader field of cryptographic security by providing practical insights and methodologies for strengthening post-quantum encryption schemes against advanced cryptanalytic attacks.