I would say it's
often the opposite, unless I'm misunderstanding you. Instead of being encapsulated "deeply" in a class ancestor, state in FP is in the "top" of the program, in the "shallow" part, as explicit as possible and as close to the entry point as possible, while the functional part is the thing that is in the middle. The term for this is "Functional core, imperative shell". In something like Haskell, side-effects are dealt with even "before" the entry point: they're handed by the runtime, which is the part that calls the entry point.
This also translates well to OOP in the form of things like hexagonal architecture (eg: business logic is pure, and state is modified by a database adapter), or to modern frontend programming (eg: the render tree is pure, visual representation state is stored/modified with by React), including flux architecture (eg: reducers are pure, state is stored/modified by Redux).
I really like this presentation about it: https://www.destroyallsoftware.com/screencasts/catalog/funct...