When CONSTRAINED_RESIZE_POLICY is set on a TableView an additional empty table column header and a horizontal scrollbar can appear. Here is an example to demonstrate the behavior:
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import javafx.application.Application;
import javafx.collections.FXCollections;
import javafx.collections.ObservableList;
import javafx.embed.swing.SwingFXUtils;
import javafx.event.ActionEvent;
import javafx.event.EventHandler;
import javafx.geometry.Insets;
import javafx.scene.Scene;
import javafx.scene.SnapshotResult;
import javafx.scene.control.Button;
import javafx.scene.control.TableColumn;
import javafx.scene.control.TableView;
import javafx.scene.control.cell.PropertyValueFactory;
import javafx.scene.image.WritableImage;
import javafx.scene.layout.VBox;
import javafx.scene.paint.Color;
import javafx.stage.Stage;
import javafx.util.Callback;

import javax.imageio.ImageIO;
import java.io.File;
import java.io.IOException;

public class TableViewSizeDemo extends Application {


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

	@Override
	public void start(final Stage stage) throws Exception {
		stage.setTitle("TableView Demo");

		VBox pane = new VBox();
		pane.setPadding(new Insets(10));

		ObservableList<Person> items = FXCollections.observableArrayList(people(100));
		final TableView<Person> tableView = new TableView<>(items);
		tableView.setColumnResizePolicy(TableView.CONSTRAINED_RESIZE_POLICY);

		final TableColumn<Person, String> firstNameColumn = new TableColumn<>("First Name");
		firstNameColumn.setCellValueFactory(new PropertyValueFactory<>("firstName"));
		final TableColumn<Person, String> lastNameColumn = new TableColumn<>("Last Name");
		lastNameColumn.setCellValueFactory(new PropertyValueFactory<>("lastName"));

		tableView.getColumns().addAll(firstNameColumn, lastNameColumn);

		Button button = new Button("take snapshot");
		button.setOnAction(new EventHandler<ActionEvent>() {
			@Override
			public void handle(final ActionEvent event) {

				WritableImage wim = new WritableImage(300, 500);
				stage.getScene().snapshot(new Callback<SnapshotResult, Void>() {
					@Override
					public Void call(final SnapshotResult param) {
						try {
							ImageIO.write(SwingFXUtils.fromFXImage(wim, null), "png", new File("tableview_constrained_resize_policy.png"));
						} catch (IOException e) {
							e.printStackTrace();
						}
						return null;
					}
				}, wim);


			}
		});

		pane.getChildren().addAll(tableView, button);

		Scene scene = new Scene(pane, 300, 500, Color.DODGERBLUE);
		stage.setScene(scene);
		stage.show();
	}

	public static ObservableList<Person> people(int howMany) {
		ObservableList<Person> result = FXCollections.observableArrayList();
		for (int i = 0; i < howMany; i++) {
			result.add(new Person("firstname " + i, "lastname " + i));

		}
		return result;
	}

	public static class Person {
		private final String firstName;
		private final String lastName;

		public Person(final String firstName, final String lastName) {
			this.firstName = firstName;
			this.lastName = lastName;
		}

		public String getFirstName() {
			return firstName;
		}

		public String getLastName() {
			return lastName;
		}
	}

}

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I think it would make sense that the additional table column header would never appear and then
also the horizontal scrollbar should not appear.

With the current behavior when the horizontal scrollbar is moved to the right the additional column header appears. Also note that when the table loses the focus the horizontal scrollbar moves to the left but the
additional column header stays visible.