Generative AI lowers listing and migration frictions in digital marketplaces. We ask whether faster seller churn improves market health or depletes opportunities faster. In an agent-based model, AI affects only launch cost C_L and migration time T_M; sellers chase transient product windows, consumers update trust, new opportunities arrive at rate λ_P , and the platform moderates at intensity φ. Higher AI assistance increases migrations but not bankruptcy survival when the catalog is finite and unreplenished. Collective churn can yield zombie markets: solvent sellers, near-zero active products, and collapsed assortment diversity. Replenishment and governance jointly bound outcomes: low λ_P drives exhaustion; only a narrow band of moderate φ keeps trust, participation, and diversity positive simultaneously. Platform health must be judged on activity and diversity together with trust, not on trust or seller survival alone.