To reproduce on attached app:
 - resize application window wide enough to not shrink a TabPane;
 - select any tab;
 - resize application window narrow enough to shrink a TabPane;
 - select any tab;
 - press drop-down menu menu button

import javafx.application.Application;
import javafx.event.ActionEvent;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.control.ContextMenu;
import javafx.scene.control.Label;
import javafx.scene.control.MenuItem;
import javafx.scene.control.Tab;
import javafx.scene.control.TabPane;
import javafx.scene.input.KeyCombination;
import javafx.stage.Stage;

public class Main extends Application {

    @Override public void start(Stage stage) {
        TabPane tabs = new TabPane();
        for (int i=0; i<7; i++) {
            Label label = new Label("Label" + i);
            Tab tab = new Tab("Tab" + i);
            tab.setContent(label);
            tabs.getTabs().add(tab);
        }
        stage.setScene(new Scene(tabs));
        stage.sizeToScene();
        stage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }
}

java.lang.NullPointerException
        at com.sun.javafx.scene.control.skin.TabPaneSkin$TabControlButtons$1.handle(TabPaneSkin.java:1297)
        at com.sun.javafx.scene.control.skin.TabPaneSkin$TabControlButtons$1.handle(TabPaneSkin.java:1295)
        at com.sun.javafx.event.CompositeEventHandler.dispatchBubblingEvent(CompositeEventHandler.java:69)
        at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:217)
        at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:170)
        at com.sun.javafx.event.CompositeEventDispatcher.dispatchBubblingEvent(CompositeEventDispatcher.java:38)
        at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:37)
        at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
        at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
        at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
        at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
        at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
        at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:35)
        at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:92)
        at com.sun.javafx.event.EventUtil.fireEventImpl(EventUtil.java:53)
        at com.sun.javafx.event.EventUtil.fireEvent(EventUtil.java:33)
        at javafx.event.Event.fireEvent(Event.java:171)
        at javafx.scene.Scene$ClickGenerator.postProcess(Scene.java:2649)
        at javafx.scene.Scene$ClickGenerator.access$6200(Scene.java:2583)
        at javafx.scene.Scene$MouseHandler.process(Scene.java:2904)
        at javafx.scene.Scene$MouseHandler.process(Scene.java:2689)
        at javafx.scene.Scene$MouseHandler.access$1300(Scene.java:2655)
        at javafx.scene.Scene.impl_processMouseEvent(Scene.java:1281)
        at javafx.scene.Scene$ScenePeerListener.mouseEvent(Scene.java:1913)
        at com.sun.javafx.tk.quantum.GlassViewEventHandler.handleMouseEvent(GlassViewEventHandler.java:215)
        at com.sun.glass.ui.View.handleMouseEvent(View.java:493)
        at com.sun.glass.ui.View.notifyMouse(View.java:871)
        at com.sun.glass.ui.win.WinApplication._runLoop(Native Method)
        at com.sun.glass.ui.win.WinApplication.access$100(WinApplication.java:29)
        at com.sun.glass.ui.win.WinApplication$2$1.run(WinApplication.java:62)
        at java.lang.Thread.run(Thread.java:662)