Instruction tuned reasoning models are increasingly deployed with safety classifiers trained on frozen embeddings, assuming representation stability across model updates. We systematically investigate this assumption and find it fails: normalized perturbations of magnitude $σ=0.02$ (corresponding to $\approx 1^\circ$ angular drift on the embedding sphere) reduce classifier performance from $85\%$ to $50\%$ ROC-AUC. Critically, mean confidence only drops $14\%$, producing dangerous silent failures where $72\%$ of misclassifications occur with high confidence, defeating standard monitoring. We further show that instruction-tuned models exhibit 20$\%$ worse class separability than base models, making aligned systems paradoxically harder to safeguard. Our findings expose a fundamental fragility in production AI safety architectures and challenge the assumption that safety mechanisms transfer across model versions.

Fine-tuning large language models (LLMs) for downstream tasks typically exhibit a fundamental safety-capability tradeoff, where improving task performance degrades safety alignment even on benign datasets. This degradation persists across standard approaches including supervised finetuning (SFT) and reinforcement learning from human feedback (RLHF). While reinforcement learning with verifiable rewards (RLVR) has emerged as a promising alternative that optimizes models on objectively measurable tasks, its safety implications remain unexplored. We present the first comprehensive theoretical and empirical analysis of safety properties in RLVR. Theoretically, we derive upper bounds on safety drift under KL-constrained optimization and prove conditions under which safety degradation is eliminated. Empirically, we conduct extensive experiments across five adversarial safety benchmarks, demonstrating that RLVR can simultaneously enhance reasoning capabilities while maintaining or improving safety guardrails. Our comprehensive ablation studies examine the effects of optimization algorithms, model scale, and task domains. Our findings challenge the prevailing assumption of an inevitable safety capability trade-off, and establish that a specific training methodology can achieve both objectives simultaneously, providing insights for the safe deployment of reasoning-capable LLMs.