In recent years, Large Language Models (LLMs) have made significant progress in emotional support dialogue. However, there are two major challenges for LLM-based support systems. First, users may be hesitant to fully disclose their emotions at the outset. Second, direct probing or excessive questioning can induce discomfort or even resistance. To bridge this gap, we propose COCOON, a proactive emotional support framework that leverages principles of active listening to uncover implicit user needs. We design a multi-stage data curation pipeline and an annotation mechanism for support strategies. Based on this framework, we build COCOON-Llama3, a fine-tuned large language model, and evaluate it using both standard metrics and psychological scales. Experimental results indicate that our model more effectively elicits implicit emotional needs and delivers empathetic support compared to existing baselines, suggesting its utility for building more inclusive emotional support dialogue systems.