Shadow model attacks are the state-of-the-art approach for membership inference attacks on machine learning models. However, these attacks typically assume an adversary has access to a background (nonmember) data distribution that matches the distribution the target model was trained on. We initiate a study of membership inference attacks where the adversary or auditor cannot access an entire subclass from the distribution -- a more extreme but realistic version of distribution shift than has been studied previously. In this setting, we first show that the performance of shadow model attacks degrades catastrophically, and then demonstrate the promise of another approach, quantile regression, that does not have the same limitations. We show that quantile regression attacks consistently outperform shadow model attacks in the class dropout setting -- for example, quantile regression attacks achieve up to 11$\times$ the TPR of shadow models on the unseen class on CIFAR-100, and achieve nontrivial TPR on ImageNet even with 90% of training classes removed. We also provide a theoretical model that illustrates the potential and limitations of this approach.