It is surprisingly simple to undock the applet: the code that does this simply removes it from some mysterious container where it is attached on a browser and then is free to place it into trivial JFrame. It is even possible to reattach the applet to its browser container when the user closes this JFrame (inside the window listener).
It is more difficult to implement support, how to signal that we want to undock the applet. Oracle talks something about dragging out with ALT key pressed but with my IceTea seems not working very well - I can register mouse listener on applet but majority of mouse exit events do not get delivered. Adding a button into JLayeredPane seems more promising: inside this pane, the button is nicely over the rest of the applet, exactly in location I can set with setBounds(...) and reacts to mouse click, calling my action listener. The new problem is that the button is covering part of the applet interface; thinking that to do now. Maybe the button can be auto-hidded after several seconds of run.