This paper addresses the issue of reliability in Industrial Internet of Things (IIoT) in case of missing sensors measurements due to network or hardware problems. We propose to support the fault detection and classification modules, which are the two critical components of a monitoring system for IIoT, with a generative model. The latter is responsible of imputing missing sensor measurements so that the monitoring system performance is robust to missing data. In particular, we adopt Generative Adversarial Networks (GANs) to generate missing sensor measurements and we propose to fine-tune the training of the GAN based on the impact that the generated data have on the fault detection and classification modules. We conduct a thorough evaluation of the proposed approach using the extended Tennessee Eastman Process dataset. Results show that the GAN-imputed data mitigate the impact on the fault detection and classification even in the case of persistently missing measurements from sensors that are critical for the correct functioning of the monitoring system.