This study investigates the vulnerabilities of data-driven offline signature verification (DASV) systems to generative attacks and proposes robust countermeasures. Specifically, we explore the efficacy of Variational Autoencoders (VAEs) and Conditional Generative Adversarial Networks (CGANs) in creating deceptive signatures that challenge DASV systems. Using the Structural Similarity Index (SSIM) to evaluate the quality of forged signatures, we assess their impact on DASV systems built with Xception, ResNet152V2, and DenseNet201 architectures. Initial results showed False Accept Rates (FARs) ranging from 0% to 5.47% across all models and datasets. However, exposure to synthetic signatures significantly increased FARs, with rates ranging from 19.12% to 61.64%. The proposed countermeasure, i.e., retraining the models with real + synthetic datasets, was very effective, reducing FARs between 0% and 0.99%. These findings emphasize the necessity of investigating vulnerabilities in security systems like DASV and reinforce the role of generative methods in enhancing the security of data-driven systems.