Generative adversarial networks (GANs) have ushered in a revolution in image-to-image translation. The development and proliferation of GANs raises an interesting question: Can we train a GAN to remove an object, if present, from an image while otherwise preserving the image? Specifically, can a GAN ''virtually heal'' anyone by turning his medical image, with an unknown health status (diseased or healthy), into a healthy one, so that diseased regions could be revealed by subtracting those two images? Such a task requires a GAN to identify a minimal subset of target pixels for domain translation, an ability that we call fixed-point translation, which no GAN is equipped with yet. Therefore, we propose a new GAN, called Fixed-Point GAN, trained by (1) supervising same-domain translation through a conditional identity loss, and (2) regularizing cross-domain translation through revised adversarial, domain classification, and cycle consistency loss. Based on fixed-point translation, we further derive a novel framework for disease detection and localization using only image-level annotation. Qualitative and quantitative evaluations demonstrate that the proposed method outperforms the state of the art in multi-domain image-to-image translation and that it surpasses predominant weakly-supervised localization methods in both disease detection and localization. Implementation is available at https://github.com/jlianglab/Fixed-Point-GAN.