That’s a good analogy. Functions calling other functions is similar to classes subclassed from other classes. Changes to the lowest-level function can have undesirable rippling effects. Changes to the base class behaviour can also have undesirable consequences. That’s why your base class behaviour should never have breaking changes. If it does, then you’ve designed your class hierarchy incorrectly.
Good OOP requires good and thoughtful design. Good FP does, as well. There is no room for sloppiness in programming.