Post-train pruning without fine-tuning has emerged as an efficient method for compressing large language models for inference, offering a computationally cheaper alternative to other approaches. However, recent studies have revealed that, unlike quantization, pruning consistently degrades model performance as sparsity increases. We demonstrate that this degradation results from pruning’s inability to preserve a low-rank structure in the model's weights, which is crucial for maintaining attention sinks. Furthermore, we show that these attention sinks play a key role in enabling the model to segment sequences—an essential mechanism for effective few-shot learning.