The benignity conjecture for subsets of models of stable theories

Let $T$ be a stable theory, let $M$ be a model of $T$, and let $A\subseteq M$. The set $A$ is benign in $M$ if equality of types over $A$ implies equality of the corresponding types in the language expanded by a predicate for $A$. The benignity conjecture. Every subset $A\subseteq M$ is benign. Shelah observed a counterexample: there is an $\omega$-stable rank-$2$ theory with ndop having a model and a subset that is not benign. Thus the conjecture is refuted.