Vision-language-action (VLA) policies operate in a closed loop in real-world robot tasks: a robot observes the scene, executes an action chunk, and conditions its next decision on the resulting observation. However, most existing world models for robot action evaluation are limited to open-loop prediction along pre-collected action trajectories. This prevents them from supporting closed-loop VLA evaluation, where each action chunk must be conditioned on the observation generated by the previous execution. To address this gap, we propose PiL-World, a chunk-wise world model designed for policy-in-the-loop VLA evaluation. Given the current observation and the action trajectory rolled out by a VLA policy, PiL-World generates multi-view future observations that are consistent with the VLA rollout and match the image inputs required by the policy. By alternating between VLA inference and world-model prediction, PiL-World enables closed-loop evaluation without real robot execution at every step. To improve rollout fidelity, PiL-World conditions video generation on action-derived visual control from head-view robot motion and latent histories that encode task execution context, while jointly predicting complementary multi-view observations. Beyond successful teleoperated demonstrations, it also learns from failed execution trajectories, helping the imagined rollouts better match the distribution of real policy executions. We evaluate PiL-World on three real dual-arm manipulation tasks. PiL-World generates imagined rollouts that are highly consistent with real robot executions. More importantly, compared with the baseline, it reduces the error between VLA success rates measured in real-world rollouts and those estimated through closed-loop world-model evaluation from 63.2% to 12.0%.