Is it possible to have a single iPhone screen with its view loaded from a xib by that screen's UIViewController, but then another UIView within that screen with content loaded from a separate xib file? If so, is it possible to have that nested view's events handled by a separate custom UIViewController subclass from the rest of the screen? If both of these things are possible, are they also advisable?
It is possible. Apple suggests against having more than one UIViewController active on screen at once, so they would advise against. I would suggest only doing it if the reason for the second view controller is navigation or modal.
A view controller with the purpose of loading other view controllers, like a navigation controller, needs some screen space for itself and uses the rest to load another view controller. That is fine. The criteria here is that only one controller is presenting content while the other is presenting navigation.
A view controller could load another view controller to perform some limited task like selecting an item from a list or entering some text. The second view controller might only fill part of the screen. The criteria here is that the one controller behaves modally and will only be displayed long enough to get some user input.
As for the general case of splitting the screen between two view controllers that are presenting content, the Apple suggestion is that you have a single class derived from UIViewController manage the views. If the view is complex enough to warrant other controllers, then derive them from NSObject and have the master view controller manage the child controllers along with the views. The child controllers would have the master controller as a delegate, and the master controller would pass views to the child controllers to manage but not own.