ADDITIONAL SYSTEM INFORMATION :
Tested and reproducible on Java 8, 11 and 15 with Linux and Windows 10 with according according JavaFX.

A DESCRIPTION OF THE PROBLEM :
When "window.close()" in JavaScript is called within a webpage loaded into a WebEngine-instance, the "localStorage" (in JavaScript) will permanently become null.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
- create empty file on /tmp/foo.html (or change path, or use web URL)
- make sure user-data-directory parent is writable (/tmp/java-store)
- run main in LocalStorageBugDemo (which reads localStorage, "closes" window and reads storage again)

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
localStorage before close is: [object Storage]
localStorage before close is: [object Storage]

ACTUAL -
localStorage before close is: [object Storage]
localStorage after close is: null

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import javafx.application.Application;
import javafx.application.Platform;
import javafx.concurrent.Worker;
import javafx.scene.web.WebEngine;
import javafx.scene.web.WebView;
import javafx.stage.Stage;

import java.io.File;

public class LocalStorageBugDemo extends Application {

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

    @Override
    public void start(final Stage stage) {
        final WebView webView = new WebView();
        final WebEngine webEngine = webView.getEngine();
        webEngine.setJavaScriptEnabled(true);
        webEngine.setUserDataDirectory(new File("/tmp/java-store"));

        webEngine.load("file:///tmp/foo.html");
        webEngine.getLoadWorker().stateProperty().addListener((observable, oldValue, newState) -> {
                    if (newState == Worker.State.SUCCEEDED) {
                        System.out.println("localStorage before close is: " + webEngine.executeScript("localStorage;"));
                        webEngine.executeScript("window.close();");
                        System.out.println("localStorage after close is: " + webEngine.executeScript("localStorage;"));
                        Platform.exit();
                    }
                }
        );
    }
}
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