Event cameras provide sparse yet temporally high-temporal-resolution motion information, demonstrating great potential for motion deblurring. Existing methods focus on cross-modal interaction, overlooking the inherent incompleteness of event streams, which arises from the trade-off between sensitivity and noise introduced by the thresholding mechanism of Dynamic Vision Sensors (DVS). Such degradation compromises the integrity of motion priors and limits the effectiveness of event-guided deblurring. To tackle these challenges, we propose a Robust Event-guided Deblurring (RED) network with modality-specific disentangled representation. First, we introduce a Robustness-Oriented Perturbation Strategy (RPS) that applies random masking to events, which exposes RED to incomplete patterns and then foster robustness against various unknown scenariothis http URL, a disentangled OmniAttention is presented to explicitly model intra-motion, inter-motion, and cross-modality correlations from two inherently distinct but complementary sources: blurry images and partially disrupted events. Building on these reliable features, two interactive modules are designed to enhance motion-sensitive areas in blurry images and inject semantic context into incomplete event representations. Extensive experiments on synthetic and real-world datasets demonstrate RED consistently achieves state-of-the-art performance in both accuracy and robustness.