You’re right that masks don’t have any such functionality built-in.
You might be able to accomplish something like this with expressions.
And I have a feeling that if this is possible, it might involve the Reshape effect, which is a warping tool that utilizes masks. You might be able, via expressions, to link a mask in one comp to the mask used in the reshape effect in another comp.
You might want to pose this question in the Expressions forum.