Multi-agent LLM systems often treat consensus as evidence of successful interaction. For deliberative problems, however, reliability depends on whether agents preserve the facts and viewpoints needed to interpret an issue. We identify the deliberative illusion: discussion produces (1) factual attrition, the progressive loss of issue-critical facts, alongside (2) stance homogenization, the collapse of diverse positions toward consensus. To measure this process, we introduce DelibTrace, a framework that decomposes each issue into atomic facts, labels issue-critical ones, distributes them across agents, and tracks their survival across discussion rounds. Across ethical and news-based deliberation with three representative LLM families, multi-agent discussion erases up to 72% of issue-critical facts. This loss is consequential: retained evidence can reconstruct the issue misleadingly, final stances remain anchored in base-model priors, and a single malicious agent can inject misinformation into the shrinking shared context. These results reveal a sharper risk: agents can agree more while knowing less. We call for evaluations that measure which facts, uncertainties, and legitimate disagreements survive interaction.