The solutions to these problems in "extending and refactoring" are the same in dynamically and statically typed languages because in both you have to make sure

The solutions to these problems in "extending and refactoring" are the same in dynamically and statically typed languages because in both you have to make sure functions/methods get the correctly typed input and return some expected type as output. In both worlds you will either refactor everything, abstract the problem away with interfaces or union types or you'll do type conversions at the boundaries of the code you touch. That layer is there anyway, except for your interpreter of a dynamic language only knows about problems at run-time, while the compiler that checks a static type system will tell you at compile-time.