Motivated by the efficiency and rapid convergence of pre-trained models for solving downstream tasks, this paper extensively studies the impact of Continual Learning (CL) models as pre-trainers. We find that, in both supervised and unsupervised CL, the transfer quality of representations does not show a noticeable degradation of fine-tuning performance but rather increases gradually. This is because CL models can learn improved task-general features when easily forgetting task-specific knowledge. Based on this observation, we suggest a new unsupervised CL framework with masked modeling, which aims to capture fluent task-generic representation during training. Furthermore, we propose a new fine-tuning scheme, GLobal Attention Discretization (GLAD), that preserves rich task-generic representation during solving downstream tasks. The model fine-tuned with GLAD achieves competitive performance and can also be used as a good pre-trained model itself. We believe this paper breaks the barriers between pre-training and fine-tuning steps and leads to a sustainable learning framework in which the continual learner incrementally improves model generalization, yielding better transfer to unseen tasks.