With the growing adoption of reinforcement learning with human feedback (RLHF) for aligning large language models (LLMs), the risk of backdoor installation during alignment has increased, leading to unintended and harmful behaviors. Existing backdoor triggers are typically limited to fixed word patterns, making them detectable during data cleaning and easily removable post-poisoning. In this work, we explore the use of prompt-specific paraphrases as backdoor triggers, enhancing their stealth and resistance to removal during LLM alignment. We propose AdvBDGen, an adversarially fortified generative fine-tuning framework that automatically generates prompt-specific backdoors that are effective, stealthy, and transferable across models. AdvBDGen employs a generator-discriminator pair, fortified by an adversary, to ensure the installability and stealthiness of backdoors. It enables the crafting and successful installation of complex triggers using as little as 3% of the fine-tuning data. Once installed, these backdoors can jailbreak LLMs during inference, demonstrate improved stability against perturbations compared to traditional constant triggers, and are more challenging to remove. These findings underscore an urgent need for the research community to develop more robust defenses against adversarial backdoor threats in LLM alignment.