Dealing with extreme values is a major challenge in probabilistic modeling, of great importance in various application domains such as economics, engineering and life sciences. In the context of Generative Modeling, it is known that models based on transformations of light-tailed distribution, such as Generative Adversarial Networks (GANs), fail to capture the behaviour in the tails. In particular, these models are not able to capture the dependence in extreme regions. We study a modified version of the GAN algorithm, where the input is a heavy-tailed distribution (and we call it HTGAN). Recalling the stable tail dependence function (stdf), a tool from extreme-value theory that measures the dependence structure in extreme regions, we provide a bound on the approximation of the stdf of the target with the output of a HTGAN.This bound scales as $N^{{-1}/{(d -1)}}$, where $N$ is the dimension of the input noise of the network and $d$ is the dimension of the data of interest. This suggests increasing the dimension of the latent noise to gain precision in the estimation of dependence. We perform experiments, comparing HTGAN with a classical light-tailed GAN (LTGAN) on both synthetic and real datatets exhibiting heavy-tailed characteristics. These experiments confirm our theoretical findings: First, the HTGAN algorithm is better at reproducing dependence in extremes than LTGAN. Second, we show that the quality of approximation gets better as the dimension of the latent noise increases.