Not as you have described, no. Function objects support very few reflective methods, most of which are deprecated or obsolete. There is a good reason for this: while closures are a common way to implement lexically scoped functions, they are not the only way, and in some cases they may not be the fastest. Javascript probably avoids exposing such details to allow implementations more flexibility to improve performance.
That said, you can get around this in various ways. One approach is to add an argument to the inner function telling it that it should return the value of a certain variable rather than doing what it usually does. Alternatively, you can store the variable alongside the function.
For an example of an alternative implementation technique, look up "lambda lifting". Some implementations may use different approaches in different situations.
Edit
An even better reason not to allow that sort of reflection is that it breaks the function abstraction rather horribly, and in doing so exposes hairy details of how the function was produced. If you want that sort of access, you really want an object, not a function.