Average segmentation accuracy and model count do not reveal whether models fail on the same cases. We present CoFailMed, an audit of correlated failures in pretrained-encoder pools for medical segmentation. Across five 2D tasks, we evaluate 11 public pretrained encoders (a controlled sample, not a census) using frozen features and separately trained $1\times 1$ readouts with four seeds per encoder. Shared-checkpoint pairs have the highest mean per-case Dice correlation. An expanded 17-encoder analysis shows that distinct checkpoints within the same encoder family remain more correlated than cross-family pairs. At the pooled 33rd-percentile Dice threshold, four-member pools drawn from distinct encoders have mean effective sizes of 1.56-2.92, estimated from failure correlations in pools with enough failures and passes per member. In the primary pool, richer readouts and fine-tuning narrow the Dice-correlation gap between pairs sharing a checkpoint (or the DINOv2-B/S release) and all other pairs. Yet dependence between different encoders can increase, and fine-tuning does not consistently increase effective pool size at 33rd-percentile thresholds recomputed for each training recipe. A smaller between-group gap can coexist with greater dependence. Pool evaluation should therefore report absolute dependence and threshold-specific effective size alongside accuracy and nominal pool size. The CoFailMed release provides aligned per-case traces, analysis scripts and study code to reproduce the central audit results.

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