When data distributions shift between training and testing in arbitrary, unconstrained ways, learning a robust classifier is fundamentally impossible. For instance, in a binary classification task like distinguishing cats from dogs, if the input distribution $p_S(\mathbf{x}) = p_T(\mathbf{x})$ remains exactly the same but all labels are deterministically flipped such that $p_S(y \mid \mathbf{x}) = 1 - p_T(y \mid \mathbf{x})$, an algorithm cannot distinguish this pathological scenario from one where the distribution never changed at all.