Multimodal Industrial Anomaly Detection (MIAD)-fusing 3D point clouds and 2D RGB for product defect detection-is critical to quality inspection. However, existing MIAD methods assume all modalities are available and paired, overlooking real-scenario modality-missing and risking overfitting to incomplete data. To address these, we conduct the first comprehensive study on Modality-Incomplete Industrial Anomaly Detection (MIIAD) and establish MIIAD Bench , a benchmark covering diverse missing settings. Meanwhile, we propose RADAR, a robust two-stage Robust modAlity-instructive fusing & Detecting frAmewoRk. RADAR integrates i) a Modality-Incomplete Instruction mechanism-guiding the multimodal Transformer to focus more on available modal info, and ii) a Double-Pseudo Hybrid Module to highlight unique modality combinations and reduce overfitting. Our results show RADAR outperforms prior methods markedly on MIIAD Bench.