I've attached a sample testcase:

Run the applet
Click the button:
FileSaveService is called, trying to save a file on the local filesystem.
                try {
                        FileSaveService fileSaveService = (FileSaveService) ServiceManager.lookup("javax.jnlp.FileSaveService");
                        ByteArrayOutputStream os = new ByteArrayOutputStream();
                        os.write(10);
                        InputStream imageInputStream = new ByteArrayInputStream(os.toByteArray());
                        String[] extenstions = {"png"};
                        fileSaveService.saveFileDialog(null, extenstions, imageInputStream, "name.png");
                } catch(Exception e) {
                    logger.log(Level.WARNING, e.toString(), e);
                }

RESULT:
A security dialog is shown requesting for a filesytem access -> User clicks 'OK" -> JVM and browser hang and the applet freezes, no FileChooser is shown

The same code works under Windows