In recent years, curve estimation-based low-light image enhancement methods have gained increasing attention due to they do not need reference images for training. However, existing methods often encounter issues such as overexposure, color distortion, and artifacts when processing images with uneven luminance distribution. To address this issue, this paper proposes an approximate global convergence curve estimation based unsupervised low-light image enhancement method, called Harnessing Elastic Adaptive Learning Network (HEAL-Net). Specifically, we design an Approximate Global Convergence Curve (AGC-Curve) to reduce the model's sensitivity to input variations. Additionally, we introduce a Dynamic Deep Feature Mapping (DDFM) branch, which further smooths the luminance distribution by capturing the correlations between color channels. Experimental results demonstrate that our method achieves advanced performance across multiple benchmarks and exhibits strong robustness to inputs with uneven luminance distribution.