The pattern you're asking about is not really native to the way JSF works.
Request-based frameworks like Struts and Spring MVC, and the older Model-2 Servlet/JSP based approach did work like this.
In JSF, first and foremost it's the page (view) that's automatically mapped to a request URL. There's no notion of a bean that's directly mapped to a URL and also there's no notion of a bean that has a framework enforced 1:1 relation with a view. There is the concept of a backing bean though, but this is by convention. For JSF, all beans are "helper beans" that are merely referenced by the view.
BalusC outlined the popular ways that can be used today to get some of the behavior from request-based frameworks in JSF in his answer. JSF 2.2 will slightly expand on this support via the introduction of view actions, which formalizes a few of the typical use cases for the preRenderViewEvent
.
That said, JSF is a very flexible framework and very few things are set in stone. A lot of JSF's behavior can be replaced or added to via an elaborate plug-in and decorator system.
For this use case, the fact that JSF binds URLs to (Facelets) views can be overridden, and you can in fact let beans directly react to requests. Although for a slightly different purpose, this is what I essentially did for JavaVDL, by overriding the so-called view handler.
You do have to ask yourself if this is really what you want to do, and if you want to work in this way whether JSF is the best choice for you. But via the methods outlined in JavaVDL (sourcecode here), you should be able to do this. Do note that this last method is not suited for beginners and requires quite a lot of JSF experience if you want to pull this off yourself. (If you, or anyone else would like to have this functionality, please consider creating an issue for it at the OmniFaces issues list).