The depth/thermal information is beneficial for detecting salient object with conventional RGB images. However, in dual-modal salient object detection (SOD) model, the robustness against noisy inputs and modality missing is crucial but rarely studied. To tackle this problem, we introduce \textbf{Co}nditional Dropout and \textbf{LA}nguage-driven(\textbf{CoLA}) framework comprising two core components. 1) Language-driven Quality Assessment (LQA): Leveraging a pretrained vision-language model with a prompt learner, the LQA recalibrates image contributions without requiring additional quality annotations. This approach effectively mitigates the impact of noisy inputs. 2) Conditional Dropout (CD): A learning method to strengthen the model's adaptability in scenarios with missing modalities, while preserving its performance under complete modalities. The CD serves as a plug-in training scheme that treats modality-missing as conditions, strengthening the overall robustness of various dual-modal SOD models. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art dual-modal SOD models, under both modality-complete and modality-missing conditions.