Reproducer:

Button button = new Button("Click");
button.setOnAction(e -> {
final Dialog<Object> dialog = new Dialog<>();
dialog.initOwner(primaryStage);
// dialog.initStyle(StageStyle.EXTENDED); // uncomment for bug
dialog.initModality(Modality.NONE);
dialog.setResizable(true); // This is important
dialog.getDialogPane().getButtonTypes().addAll(ButtonType.OK);
dialog.setOnCloseRequest(dialogEvent -> {
System.out.println("Close the dialog pane. This is not called when EXTENDED is used.");
});
dialog.show();
});

StackPane root = new StackPane(button);
Scene scene = new Scene(root, 300, 200);
primaryStage.setScene(scene);
primaryStage.show();