Machine unlearning aims to remove targeted concepts from a trained model while preserving the rest of its knowledge. Central challenge of this setting is that effective and robust erasure requires extensive parameter updates, which can unintentionally alter representations that should be retained. As a result, existing methods often trade erasure strength for preservation, due to the lack of formal guarantees on the protection of neutral concepts. To address this, we propose BARRIER (Bounded Activation Regions for Robust Information Erasure), a method that enables more intensive unlearning by driving updates within an identified activation space control region, where target erasure can be performed with limited collateral degradation. Using interval arithmetic, we obtain a closed-form bound on the worst-case representation change over protected regions and use it as a knowledge preservation objective. We provide a formal analysis of this protection and its effect on the functional drift. BARRIER is principled, architecture-agnostic, and compatible with existing erasure objectives. Empirical evaluations demonstrate that BARRIER achieves competitive performance across classification and generative settings, including notable gains in some cases, while maintaining strong robustness against adversarial recovery attacks. Our code is available at https://github.com/OneAndZero24/BARRIER.

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