AI memory personalizes assistants, yet users want some disclosed information forgotten. We characterize the negative space of AI memory, where protection should take precedence over potential future personalization benefits. From 179 incidents reported by 146 users, we developed a taxonomy of 15 information categories users want excluded from memory, revealing sensitivity concerns beyond conventional taxonomies. We operationalize this taxonomy in FENCE, a policy-level memory gate that automatically applies user-selected category-based rules to subsequent conversations, preventing information from protected conversations from entering AI memory by default while allowing case-by-case overrides. In a within-subjects study (N=15), participants described FENCE as making memory governance more usable, interpretable, and trustworthy than conventional post-hoc management. Our findings demonstrate how taxonomy-based rules can potentially support user-defined memory boundaries. We call for collective efforts to establish policies governing what AI should not remember, rather than leaving protection to individual retrospective management.

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