Logic locking secures hardware designs in untrusted foundries by incorporating key-driven gates to obscure the original blueprint. While this method safeguards the integrated circuit from malicious alterations during fabrication, its influence on data confidentiality during runtime has been ignored. In this study, we employ path sensitization to formally examine the impact of logic locking on confidentiality. By applying three representative logic locking mechanisms on open-source cryptographic benchmarks, we utilize an automatic test pattern generation framework to evaluate the effect of locking on cryptographic encryption keys and sensitive data signals. Our analysis reveals that logic locking can inadvertently cause sensitive data leakage when incorrect logic locking keys are used. We show that a single malicious logic locking key can expose over 70\% of an encryption key. If an adversary gains control over other inputs, the entire encryption key can be compromised. This research uncovers a significant security vulnerability in logic locking and emphasizes the need for comprehensive security assessments that extend beyond key-recovery attacks.