We propose preventive learning as the first framework to guarantee Deep Neural Network (DNN) solution feasibility for optimization problems with linear constraints without post-processing, upon satisfying a mild condition on constraint calibration. Without loss of generality, we focus on problems with only inequality constraints. We systematically calibrate the inequality constraints used in training, thereby anticipating DNN prediction errors and ensuring the obtained solutions remain feasible. We characterize the calibration rate and a critical DNN size, based on which we can directly construct a DNN with provable solution feasibility guarantee. We further propose an Adversarial-Sample Aware training algorithm to improve its optimality performance. We apply the framework to develop DeepOPF+ for solving essential DC optimal power flow problems in grid operation. Simulation results over IEEE test cases show that it outperforms existing strong DNN baselines in ensuring 100\% feasibility and attaining consistent optimality loss (<0.19%) and speedup (up to x228) in both light-load and heavy-load regimes, as compared to a state-of-the-art solver. We also apply our framework to a non-convex problem and show its performance advantage over existing schemes.