Offline Handwritten Text Recognition (HTR) systems play a crucial role in applications such as historical document digitization, automatic form processing, and biometric authentication. However, their performance is often hindered by the limited availability of annotated training data, particularly for low-resource languages and complex scripts. This paper presents a comprehensive survey of offline handwritten data augmentation and generation techniques designed to improve the accuracy and robustness of HTR systems. We systematically examine traditional augmentation methods alongside recent advances in deep learning, including Generative Adversarial Networks (GANs), diffusion models, and transformer-based approaches. Furthermore, we explore the challenges associated with generating diverse and realistic handwriting samples, particularly in preserving script authenticity and addressing data scarcity. This survey follows the PRISMA methodology, ensuring a structured and rigorous selection process. Our analysis began with 1,302 primary studies, which were filtered down to 848 after removing duplicates, drawing from key academic sources such as IEEE Digital Library, Springer Link, Science Direct, and ACM Digital Library. By evaluating existing datasets, assessment metrics, and state-of-the-art methodologies, this survey identifies key research gaps and proposes future directions to advance the field of handwritten text generation across diverse linguistic and stylistic landscapes.