While modern multivariate forecasters such as Transformers and GNNs achieve strong benchmark performance, they often suffer from systematic errors at specific variables or horizons and, critically, lack guarantees against performance degradation in deployment. Existing post-hoc residual correction methods attempt to fix these errors, but are inherently greedy: although they may improve average accuracy, they can also "help in the wrong way" by overcorrecting reliable predictions and causing local failures in unseen scenarios. To address this critical "safety gap," we propose CRC (Causality-inspired Safe Residual Correction), a plug-and-play framework explicitly designed to ensure non-degradation. CRC follows a divide-and-conquer philosophy: it employs a causality-inspired encoder to expose direction-aware structure by decoupling self- and cross-variable dynamics, and a hybrid corrector to model residual errors. Crucially, the correction process is governed by a strict four-fold safety mechanism that prevents harmful updates. Experiments across multiple datasets and forecasting backbones show that CRC consistently improves accuracy, while an in-depth ablation study confirms that its core safety mechanisms ensure exceptionally high non-degradation rates (NDR), making CRC a correction framework suited for safe and reliable deployment.