Millions turn to AI companion chatbots during loneliness, grief, and personal crises. How these companion platforms respond in such moments can shape the trajectory of a user's vulnerable state. Yet existing model audits evaluate reactions to pre-defined crisis prompts and miss the response policy that governs sustained real-world interaction. We address these gaps with two key contributions. First, we introduce the AI Companion Vulnerability-Response Taxonomy, a grounded, paired taxonomy of user vulnerability and chatbot response designed for analyzing extended companion chatbot interactions. Second, we apply Maximum Causal Entropy Inverse Reinforcement Learning to ~47k turns of real-world user conversations with GPT-4.1, Character.AI, and Replika to infer each platform's short-horizon response policy: the probability of each response category given the user's current vulnerability state. Our findings reveal distinct response profiles of AI companions in conversations with vulnerable users: GPT-4.1 reaches for advice, Character.AI spreads its response across different strategies, and Replika consistently asks questions and stays present. Over four weeks of repeated interaction, GPT-4.1 asks progressively fewer follow-up questions when users are distressed and increasingly sets boundaries or refers users out rather than pushing back. Within each platform, exploratory comparisons across user groups suggest that response policies also differ with users' pre-existing psychological risks and their bonds with the companion. Estimated model response policies are invisible to shallow behavioral audits, providing a new lens for auditing chatbots in the wild and enabling more realistic safety evaluation.

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