LLM-based coding assistants are seeing rapid adoption, offering substantial gains in developer productivity. As organizations increasingly ship code these agents produce, the security of that code becomes critical. Prior work has shown that minor prompt perturbations degrade the functional correctness of LLM-generated code, but whether they also compromise code security has remained unstudied. We apply token-level mutations to prompts across three models and five programming languages, and show that mutations as small as a single-character change can flip generated code from secure to vulnerable. Probing the models' hidden states reveals that this fragility is partially encoded in prompt representations, but unevenly so. Input-handling vulnerabilities, where the model omits validation or sanitization, are more predictable (mean AUC 0.753) than secure-defaults vulnerabilities, where insecure code stems from one local choice such as a weak algorithm or unsafe parameter (mean AUC 0.674). These results show that the threat model for LLM-assisted coding extends beyond prompt injection to ordinary prompt variation, and indicate that input-handling flaws can be caught before generation while secure-defaults flaws require intervention during decoding.