Run attached application.
Press "NONE"
In the appeared (the second) window press "FILECH"
that creates filechooser

Close the first stage and get exception:

Exception in thread "JavaFX Application Thread" java.lang.IllegalStateException: The window has already been closed
at com.sun.glass.ui.Window.checkNotClosed(Window.java:202)
at com.sun.glass.ui.Window.setEnabled(Window.java:641)
at com.sun.javafx.tk.quantum.WindowStage.setPlatformEnabled(WindowStage.java:546)
at com.sun.javafx.tk.quantum.WindowStage.setEnabled(WindowStage.java:557)
at com.sun.javafx.tk.quantum.WindowStage.setVisible(WindowStage.java:325)
at javafx.stage.Window$13.invalidated(Window.java:707)
at javafx.beans.property.BooleanPropertyBase.markInvalid(BooleanPropertyBase.java:88)
at javafx.beans.property.BooleanPropertyBase.set(BooleanPropertyBase.java:122)
at javafx.stage.Window.setShowing(Window.java:744)
at javafx.stage.Window.hide(Window.java:769)
at com.sun.javafx.stage.WindowPeerListener.closed(WindowPeerListener.java:91)
at com.sun.javafx.tk.quantum.GlassWindowEventHandler.handleWindowEvent(GlassWindowEventHandler.java:68)
at com.sun.glass.ui.Window.handleWindowEvent(Window.java:895)
at com.sun.glass.ui.Window.notifyDestroy(Window.java:810)
at com.sun.glass.ui.mac.MacWindow._close(Native Method)
at com.sun.glass.ui.Window.close(Window.java:215)
at com.sun.javafx.tk.quantum.WindowStage.close(WindowStage.java:502)
at javafx.stage.Window$13.invalidated(Window.java:723)
at javafx.beans.property.BooleanPropertyBase.markInvalid(BooleanPropertyBase.java:88)
at javafx.beans.property.BooleanPropertyBase.set(BooleanPropertyBase.java:122)
at javafx.stage.Window.setShowing(Window.java:744)
at javafx.stage.Window.hide(Window.java:769)
at com.sun.javafx.stage.WindowCloseRequestHandler.dispatchBubblingEvent(WindowCloseRequestHandler.java:24)
at com.sun.javafx.event.CompositeEventDispatcher.dispatchBubblingEvent(CompositeEventDispatcher.java:38)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:37)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.EventUtil.fireEventImpl(EventUtil.java:47)
at com.sun.javafx.event.EventUtil.fireEvent(EventUtil.java:28)
at javafx.event.Event.fireEvent(Event.java:171)
at com.sun.javafx.stage.WindowPeerListener.closing(WindowPeerListener.java:84)
at com.sun.javafx.tk.quantum.GlassWindowEventHandler.handleWindowEvent(GlassWindowEventHandler.java:71)
at com.sun.glass.ui.Window.handleWindowEvent(Window.java:895)
at com.sun.glass.ui.Window.notifyClose(Window.java:801)
at com.sun.glass.ui.mac.MacCommonDialogs._showFileOpenChooser(Native Method)
at com.sun.glass.ui.mac.MacCommonDialogs.showFileChooser_impl(MacCommonDialogs.java:47)
at com.sun.glass.ui.mac.MacApplication.staticCommonDialogs_showFileChooser(MacApplication.java:303)
at com.sun.glass.ui.CommonDialogs.showFileChooser(CommonDialogs.java:127)
at com.sun.javafx.tk.quantum.QuantumToolkit.showFileChooser(QuantumToolkit.java:1354)
at javafx.stage.FileChooser.showDialog(FileChooser.java:264)
at javafx.stage.FileChooser.showOpenDialog(FileChooser.java:213)
at modalityapplication.ModalityWindow.createSubFileChooser(ModalityWindow.java:289)
at modalityapplication.ModalityWindow.access$200(ModalityWindow.java:35)
at modalityapplication.ModalityWindow$1.run(ModalityWindow.java:88)
at modalityapplication.ModalityWindow$3.handle(ModalityWindow.java:162)
at modalityapplication.ModalityWindow$3.handle(ModalityWindow.java:160)
at com.sun.javafx.event.CompositeEventHandler.dispatchBubblingEvent(CompositeEventHandler.java:60)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:162)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:115)
at com.sun.javafx.event.CompositeEventDispatcher.dispatchBubblingEvent(CompositeEventDispatcher.java:38)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:37)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.EventUtil.fireEventImpl(EventUtil.java:47)
at com.sun.javafx.event.EventUtil.fireEvent(EventUtil.java:28)
at javafx.event.Event.fireEvent(Event.java:171)
at javafx.scene.Node.fireEvent(Node.java:5919)
at javafx.scene.control.Button.fire(Button.java:179)
at com.sun.javafx.scene.control.behavior.ButtonBehavior.mouseReleased(ButtonBehavior.java:189)
at com.sun.javafx.scene.control.skin.SkinBase$5.handle(SkinBase.java:318)
at com.sun.javafx.scene.control.skin.SkinBase$5.handle(SkinBase.java:311)
at com.sun.javafx.event.CompositeEventHandler.dispatchBubblingEvent(CompositeEventHandler.java:56)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:162)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:115)
at com.sun.javafx.event.CompositeEventDispatcher.dispatchBubblingEvent(CompositeEventDispatcher.java:38)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:37)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
at com.sun.javafx.event.EventUtil.fireEventImpl(EventUtil.java:47)
at com.sun.javafx.event.EventUtil.fireEvent(EventUtil.java:33)
at javafx.event.Event.fireEvent(Event.java:171)
at javafx.scene.Scene$MouseHandler.process(Scene.java:2776)
at javafx.scene.Scene$MouseHandler.process(Scene.java:2597)
at javafx.scene.Scene$MouseHandler.access$1300(Scene.java:2570)
at javafx.scene.Scene.impl_processMouseEvent(Scene.java:1252)
at javafx.scene.Scene$ScenePeerListener.mouseEvent(Scene.java:1857)
at com.sun.javafx.tk.quantum.GlassViewEventHandler.handleMouseEvent(GlassViewEventHandler.java:203)
at com.sun.glass.ui.View.handleMouseEvent(View.java:282)
at com.sun.glass.ui.View.notifyMouse(View.java:542)
JavaFX application launcher: calling System.exit