Generative AI systems are increasingly used by older adults with cognitive impairment for everyday tasks such as information seeking, health management, and communication. While these systems provide flexible, language-based support, their open-ended outputs introduce risks of over-reliance, misinterpretation, and inappropriate decision-making. Prior work has focused on usability and adoption, with limited attention to how system design shapes users' participation in decision-making and the distribution of agency in care contexts. We present a qualitative study of 45 individuals with cognitive impairment and their caregivers. We identify five accessibility-oriented mechanisms: AI Capability Constraint, Human Oversight Embedding, Cognitive Engagement Maintenance, Human-AI Relationship Regulation, and Risk Transparency and Control, through which systems structure interaction. These mechanisms both support and constrain users by redistributing decision-making across users and caregivers. We show that their effects vary by impairment level: while protective mechanisms support users with severe impairment, they can restrict autonomy for those with mild impairment. As impairment progresses, tensions become less visible as user participation diminishes. Our findings highlight the need for dynamic designs that balance safety and autonomy in AI-supported care.

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