If you over-ride the CloseRequestFcn you can have it do whatever you tell it. In general you should always have this function call delete on the figure if you over-ride it because that is expected behaviour and if you don't the figure will not get deleted.
So if you create a CloseRequestFcn that just does something else and does not delete the figure than it will stay alive and you can switch its 'Visible' property off and do whatever else you wish.
I do this for docking and undocking panels in one of my workflows. I have a panel that is undockable and, because it is part of the workflow I don't want the user to simply be able to delete the panel when it is an undocked figure I program the CloseRequestFcn to redock it in the main figure.
The interaction between DeleteFcn, CloseRequestFcn and one or two others that are similar can be confusing, but they are explained in the help as to when each is called and what its function is. I never remember so have to look it up each time I want to do something out of the ordinary with this.