StageController
    .createStage("estimateStage", new Stage())
    .setTitle("Смета")
    .setModality(Modality.APPLICATION_MODAL)
    .showStage("estimates/fxml/EstmateFXML.fxml");

StageController.getStage("estimateStage").setOnCloseRequest(e -> System.out.println("sdfsdf")); //Не срабатывает!

closeButton.setOnMouseClicked(mouseEvent -> StageController.closeStage("estimateStage"));

package javafxapplication24;

import java.util.logging.Level;
import java.util.logging.Logger;
import javafx.application.Application;
import static javafx.application.Application.launch;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.layout.VBox;
import javafx.scene.text.Font;
import javafx.scene.text.Text;
import javafx.stage.Stage;
import javafx.stage.WindowEvent;

public class JavaFXApplication24 extends Application {

    @Override
    public void start(Stage stage) {
        Text text = new Text("!");
        text.setFont(new Font(40));
        VBox box = new VBox();
        box.getChildren().add(text);
        final Scene scene = new Scene(box,300, 250);
        scene.setFill(null);
        stage.setScene(scene);
        stage.show();
        stage.setOnCloseRequest((WindowEvent we) -> {
            System.out.println("Stage is closing");
        });

        try {
            Thread.sleep(2000);
        } catch (InterruptedException ex) {
            Logger.getLogger(JavaFXApplication24.class.getName()).log(Level.SEVERE,null,ex);
        }
        stage.close();

    }

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