Industry 4.0 imposes strict requirements on the fifth generation of wireless systems (5G), such as high reliability, high availability, and low latency. Guaranteeing such requirements implies that system failures should occur with an extremely low probability. However, some applications (e.g., training a reinforcement learning algorithm to operate in highly reliable systems or rare event simulations) require access to a broad range of observed failures and extreme values, preferably in a short time. In this paper, we propose IL-GAN, an alternative training framework for generative adversarial networks (GANs), which leverages incremental learning (IL) to enable the generation to learn the tail behavior of the distribution using only a few samples. We validate the proposed IL-GAN with data from 5G simulations on a factory automation scenario and real measurements gathered from various video streaming platforms. Our evaluations show that, compared to the state-of-the-art, our solution can significantly improve the learning and generation performance, not only for the tail distribution but also for the rest of the distribution.