Fine-tuning large language models (LLMs) with limited data poses a practical challenge in low-resource languages, specialized domains, and constrained deployment settings. While pre-trained LLMs provide strong foundations, effective adaptation under data scarcity requires focused and efficient fine-tuning techniques. This paper presents a structured and practical survey of recent methods for fine-tuning LLMs in data-scarce scenarios. We systematically review parameter-efficient fine-tuning techniques that lower training and deployment costs, domain and cross-lingual adaptation methods for both encoder and decoder models, and model specialization strategies. We further examine preference alignment approaches that guide model behavior using limited human or synthetic feedback, emphasizing sample and compute efficiency. Throughout, we highlight empirical trade-offs, selection criteria, and best practices for choosing suitable techniques based on task constraints, including model scaling, data scaling, and the mitigation of catastrophic forgetting. The aim is to equip researchers and practitioners with actionable insights for effectively fine-tuning LLMs when data and resources are limited.

Fine-tuning Large Language Models (LLMs) on sensitive datasets carries a substantial risk of unintended memorization and leakage of Personally Identifiable Information (PII), which can violate privacy regulations and compromise individual safety. In this work, we systematically investigate a critical and underexplored vulnerability: the exposure of PII that appears only in model inputs, not in training targets. Using both synthetic and real-world datasets, we design controlled extraction probes to quantify unintended PII memorization and study how factors such as language, PII frequency, task type, and model size influence memorization behavior. We further benchmark four privacy-preserving approaches including differential privacy, machine unlearning, regularization, and preference alignment, evaluating their trade-offs between privacy and task performance. Our results show that post-training methods generally provide more consistent privacy-utility trade-offs, while differential privacy achieves strong reduction in leakage in specific settings, although it can introduce training instability. These findings highlight the persistent challenge of memorization in fine-tuned LLMs and emphasize the need for robust, scalable privacy-preserving techniques.