Globally, approximately one in three women and one in five men experience domestic violence (DV) during their lifetimes. As advocacy groups and service providers explore scalable ways to support DV survivors, chatbots are increasingly being deployed for DV support. Yet questions remain about their safety, effectiveness, and governance. We systematically identified and audited 36 DV chatbots developed in 22 countries. Drawing on publicly available data, we analyzed information about these chatbots including stated purpose, deployment context, and the presence and content of privacy policies. We then conducted usability evaluations to assess their interfaces and user experience. Finally, we conducted scenario-based audits of a purposive subset of nine LLM-powered, web-accessible chatbots in English or Spanish to evaluate their responses to DV-related and digital-safety questions. Our analyses reveal a rapidly growing but fragmented ecosystem. Multiple parties are often involved in deployment, raising complex privacy risks. Notably, 16 of the 36 chatbots lacked a privacy policy, only seven provided a privacy policy that specifically addressed the chatbot, and many failed to communicate safety-relevant limitations. Only a few chatbots asked follow-up questions to contextualize users' needs, an important safeguard for survivors' safety. This work offers a global characterization of DV chatbots, surfaces critical design and governance challenges, and advances understanding of how these tools intersect with survivors' safety. We conclude with actionable recommendations for developers, advocates, and policymakers, and call for transparent design practices and regulatory safeguards to ensure these technologies protect rather than endanger survivors.