Hah! I found it.

I am working my way through Schalk and Burns's JSF: The Complete Reference.

I skipped ahead to Chapter 10 because I promised my groupies (hah!) that I would put some juicy nuggets about custom JSF component definition in my paper for RMOUG (Rocky Mountain Oracle Users Group) in a month and a half.

So I had to study more about custom component definition.

As I worked through the chapters on that subject in this book, I got to one of the examples, and it just did not work. As I debugged the code, I saw that the component's property called listener (a MethodBinding) was being set in the component's Tag Handler class, in its setProperties() method.

Then, the component (on a different request) tried to do something with this listener value that was set...but lo! The value of this property was null.

That let me to ask a question that I have asked before, but had grown fuzzy on the answer. The question was...what scope are components at? Request? Session? Does scope even apply to this, since they are not managed beans?

The partial answer is that components by default span requests. But if you start adding extra properties to the component then you had better override a couple of properties, if your component or one of its ancestors implemented the StateHolder interface at some point. If you are extending UIInput for example, this already has implemented this.

So what are these properties you need to override? saveState() and restoreState(). In the following example, the "extra" property we are adding is called listener and is a MethodBinding object:
@Override
public void restoreState(FacesContext context, Object state) {
Object values[] = (Object[]) state;
super.restoreState(context, values[0]);
listener = (MethodBinding) values[1];
}


@Override
public Object saveState(FacesContext context) {
Object values[] = new Object[2];
values[0] = super.saveState(context);
values[1] = listener;
return (values);
}

After adding these methods, the books example worked fine.

The name of the example component was HtmlHelloInputMB if anybody else is working through that same book.

I have informed the primary author through the email given on the books website, which has all the sample code for the book by the way: http://www.jsfcompref.com/