Anthropomorphic artificial intelligence systems increasingly remember personal details, display empathy, and are engaged with as social counterparts, creating forms of risk that emerge from the evolution of the user-system relationship over time. Existing safeguards largely operate at the level of individual conversational turns and cannot determine whether a sequence of seemingly acceptable interactions is cumulatively moving a particular user toward harm. This paper introduces personalized trajectory-level safety, a framework that treats relational safety as a sequential decision problem over a latent escalation state inferred from the user's messages and influenced by the system's responses. At each turn, a screening step first discards any response strategy that does not preserve at least one safe continuation of the interaction under every plausible model of the user. Among the remaining strategies, we formulate action selection as multimodal trajectory sampling, and use a Generative Flow Network to generate diverse future evolutions in proportion to their plausibility, safety, and utility. The system then selects the strategy that preserves the largest fraction of safe and useful continuations. We evaluate the framework in simulation, calibrated on statistics reported for real human-chatbot interactions, and using response strategies derived from public benchmarks. Results show that trajectory-aware decision making substantially reduces the frequency of harmful states while keeping helpful interaction. This work reframes safety for anthropomorphic AI from response-level filtering to personalized control over the future evolution of human-AI relationships. The source code is available at https://github.com/benedettapicano/ANTHROPOMORPHIC_SAFETY_TRAJ.

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