Recently, unsupervised salient object detection (USOD) has gained increasing attention due to its annotation-free nature. However, current methods mainly focus on specific tasks such as RGB and RGB-D, neglecting the potential for task migration. In this paper, we propose a unified USOD framework for generic USOD tasks. Firstly, we propose a Progressive Curriculum Learning-based Saliency Distilling (PCL-SD) mechanism to extract saliency cues from a pre-trained deep network. This mechanism starts with easy samples and progressively moves towards harder ones, to avoid initial interference caused by hard samples. Afterwards, the obtained saliency cues are utilized to train a saliency detector, and we employ a Self-rectify Pseudo-label Refinement (SPR) mechanism to improve the quality of pseudo-labels. Finally, an adapter-tuning method is devised to transfer the acquired saliency knowledge, leveraging shared knowledge to attain superior transferring performance on the target tasks. Extensive experiments on five representative SOD tasks confirm the effectiveness and feasibility of our proposed method. Code and supplement materials are available at https://github.com/I2-Multimedia-Lab/A2S-v3.