Large language models (LLMs) often require fine-tuning (FT) to perform well on downstream tasks, but FT can induce safety-alignment drift even when the training dataset contains only benign data. Prior work shows that introducing a small fraction of harmful data can substantially compromise LLM refusal behavior, causing LLMs to comply with harmful requests. Existing defense methods often rely on model-wide interventions, such as restricting which parameters are updated or injecting additional safety data, which can limit generality and degrade downstream task performance. To address these limitations, we propose a fine-tuning framework called Preserving Safety Alignment via Constrained Tokens (PACT), which stabilizes the model's confidence on safety tokens. Our approach is motivated by the empirical observation that safety-aligned behavior is reflected in the model's token-level output confidence and is often concentrated on a small subset of safety-related tokens. During downstream fine-tuning, we regularize the fine-tuned model to match the aligned reference model's confidence on safety-related tokens at each response step, while leaving non-safety tokens largely unconstrained to allow effective task adaptation. This targeted constraint prevents alignment drift without imposing global restrictions that typically trade off with model utility. Our code is available at {https://github.com/Glresearch1/PACT}.