Can I get an unbound function from a bound function in JavaScript?

I thought it would be useful to illustrate Win32's answer with a picture.

A wrapper generated by bind makes sure your function is called with given context no matter what.
Such wrapper will always ignore its own context.

Given a chain of wrappers, any context but the innermost is lost.
Therefore, there is no way to change the context once it has been set using bind.

What the bind method basically does is something like (not exactly, because arguments are sliced to exclude the context):

function bind(context) {
    var self = this;
    return function() {
        self.apply(context, arguments);
    }
}

So basically it's returning another function which will call itself with the given context and arguments. If you then bind it again, you'll be binding this newly created function, which will be as if bind was implemented like:

 function bind(context) {
    var self = this;
    return function() {
        self.apply(context, arguments);
    }.bind(otherContext);
}

But because the inner function returned by bind acts as a closure where the original context is the one binded first (self), that one will be the context in with your function will be really executed.