Run the code:

import javafx.application.Application;
import javafx.beans.property.SimpleStringProperty;
import javafx.beans.value.ChangeListener;
import javafx.beans.value.ObservableValue;
import javafx.scene.Scene;
import javafx.scene.control.TableColumn;
import javafx.scene.control.TableView;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;
import javafx.util.Callback;

public class JavaApplication4 extends Application {

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

    @Override
    public void start(Stage stage) throws Exception {
        VBox vb = new VBox();

        TableView<String> tv = new TableView<>();

        TableColumn tc1 = new TableColumn("Strings1");
        TableColumn tc2 = new TableColumn("Strings2");
        TableColumn nested = new TableColumn("Strings nested");
        tv.getColumns().add(nested);
        nested.getColumns().addAll(tc1, tc2);

        tv.getItems().addAll("One", "Two");

        tc1.setCellValueFactory(new Callback<TableColumn.CellDataFeatures<String, String>, ObservableValue<String>>() {
            @Override
            public ObservableValue<String> call(TableColumn.CellDataFeatures<String, String> p) {
                return new SimpleStringProperty(p.getValue());
            }
        });

        tc2.setCellValueFactory(new Callback<TableColumn.CellDataFeatures<String, String>, ObservableValue<String>>() {
            @Override
            public ObservableValue<String> call(TableColumn.CellDataFeatures<String, String> p) {
                return new SimpleStringProperty(p.getValue());
            }
        });

        tc1.widthProperty().addListener(new ChangeListener() {
            @Override
            public void changed(ObservableValue ov, Object t, Object t1) {
                System.out.println("Called for column 1. New Value : " + t1);
            }
        });

        tc2.widthProperty().addListener(new ChangeListener() {
            @Override
            public void changed(ObservableValue ov, Object t, Object t1) {
                System.out.println("Called for column 2. New Value : " + t1);
            }
        });

        nested.widthProperty().addListener(new ChangeListener() {
            @Override
            public void changed(ObservableValue ov, Object t, Object t1) {
                System.out.println("Called for nested. New Value : " + t1); <- never seen this output.
            }
        });

        vb.getChildren().add(tv);

        stage.setScene(new Scene(vb, 300, 300));
        stage.show();
    }
}

I resize nested column, column1 or column2. But updates on nested column width never comes.

But I saw in internal test application, that sometimes it is updated.

Also, it affects on tests, because it makes troubles for analysing of column headers structure.