The proliferation of large language models (LLMs) has intensified concerns over model theft and license violations, necessitating robust and stealthy ownership verification. Existing fingerprinting methods either require impractical white-box access or introduce detectable statistical anomalies. We propose EverTracer, a novel gray-box fingerprinting framework that ensures stealthy and robust model provenance tracing. EverTracer is the first to repurpose Membership Inference Attacks (MIAs) for defensive use, embedding ownership signals via memorization instead of artificial trigger-output overfitting. It consists of Fingerprint Injection, which fine-tunes the model on any natural language data without detectable artifacts, and Verification, which leverages calibrated probability variation signal to distinguish fingerprinted models. This approach remains robust against adaptive adversaries, including input level modification, and model-level modifications. Extensive experiments across architectures demonstrate EverTracer's state-of-the-art effectiveness, stealthness, and resilience, establishing it as a practical solution for securing LLM intellectual property. Our code and data are publicly available at https://github.com/Xuzhenhua55/EverTracer.