When Should a World Model Trust Its Imagination? Local Empirical Support Predicts Recursive Rollout Failure

World-model planners recursively evaluate imagined states that may drift into regions weakly supported by the data used to train the model. We ask whether local empirical support at an imagined state predicts rollout-prediction failure several steps later, beyond evidence that the model is already struggling at the current step. Using average $k$-nearest-neighbor distance in learned latent space as a simple support probe, we find that local support adds predictive information beyond current one-step error, rollout position, and latent norm across multiple future offsets. The relationship transfers across five state-based MuJoCo tasks, visual inputs, deterministic residual dynamics, and a Dreamer-style recurrent state-space model (RSSM). It is not captured by the tested measures of global shift magnitude and remains partially informative after conditioning on transition disagreement and Mahalanobis distance, although the residual gain is much smaller in Hopper than in HalfCheetah. The most consistent pattern is geometric. Imagined states associated with future failure lie farther from training support across all dense state-based audits and every RSSM seed. Control experiments show that this diagnostic does not automatically yield a useful intervention. A support score can become more predictive while a fixed support penalty becomes worse, and percentile calibration can weaken an effective raw penalty. Overall, local empirical support is a reproducible forward-looking diagnostic of recursive rollout-prediction failure, while the appropriate control response must be validated separately.