People experiencing mental health crises frequently turn to open-ended generative AI (GenAI) chatbots for support. However, rather than providing immediate assistance, some GenAI chatbots are designed to respond to crisis situations in ways that minimize their developers' liability, primarily through avoidance (e.g., refusing to engage beyond templated referrals to crisis hotlines). Withholding crisis support in these cases may harm users who have no viable alternatives and reduce their motivation to seek further help. At scale, this avoidant design could undermine population mental health. We propose empowerment-oriented design principles for AI crisis support, informed by community helper models. As an initial touchpoint in help-seeking, AI chatbots can act as a supportive bridge to de-escalate crises and connect users to more reliable care. Coordination between AI developers and regulators can enable a better balance of risk mitigation and user empowerment in AI crisis support.