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Since global retraining is expensive at LLM scale, recent work has largely focused on increasingly sophisticated pruning criteria that aim to select better sparsity patterns without adaptation. We revisit this trade-off through local reconstruction: after pruning, we adapt one subset of the model parameters at a time on a calibration set, training it to match the corresponding intermediate activations of the dense model. We evaluate local reconstruction across model families and scales, up to 72B parameters, and establish three main findings. First, local reconstruction is an effective adaptation mechanism for LLMs: it matches post-pruning retraining while using over an order of magnitude less data and compute, even when using PEFT techniques. 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