### Preflight Checklist
* [x] I have read the [Contributing Guidelines](https://github.com/electron/electron/blob/master/CONTRIBUTING.md) for this project.
* [x] I agree to follow the [Code of Conduct](https://github.com/electron/electron/blob/master/CODE_OF_CONDUCT.md) that this project adheres to.
* [x] I have searched the issue tracker for an issue that matches the one I want to file, without success.

### Issue Details

* **Electron Version:** 5.0.7
* **Operating System:** Windows 10

### Expected Behavior
When I navigate a `BrowserView` to a page that has `beforeunload` and `unload` handlers, I expect that closing the window will cause them to fire.

### Actual Behavior
They do not fire when closing the window.

Notably, if I don't use `BrowserView` and just navigate the `BrowserWindow` to the page, those handlers will execute.

### To Reproduce

`npm start` the code below (in main.js). In the devtools that opens up, run `window.onbeforeunload = () => true;`, then close the window. In the working case, the window will not close. In the broken case that uses `BrowserView`, it will.

```
const { app, BrowserWindow, BrowserView } = require('electron')

function brokenCase() {
	const mainWindow = new BrowserWindow();
	const view = new BrowserView();
	mainWindow.setBrowserView(view);
	view.webContents.loadURL("https://google.com");
	view.webContents.openDevTools();
}

function workingCase() {
	const mainWindow = new BrowserWindow();
	mainWindow.webContents.loadURL("https://google.com");
	mainWindow.webContents.openDevTools();
}

app.on('ready', brokenCase)
```

Maybe related to [this comment](https://github.com/electron/electron/issues/19194#issuecomment-544407723)
shell/browser/api/electron_api_web_contents.cc
const std::string& type,
    const base::FilePath& file_system_path) {
  base::FilePath path = file_system_path;
  if (path.empty()) {
    std::vector<base::FilePath> paths;
    file_dialog::DialogSettings settings;
    settings.parent_window = owner_window();
    settings.force_detached = offscreen_;
    settings.properties = file_dialog::OPEN_DIALOG_OPEN_DIRECTORY;
    if (!file_dialog::ShowOpenDialogSync(settings, &paths))
      return;
    path = paths[0];
  }
  std::string file_system_id =
      RegisterFileSystem(GetDevToolsWebContents(), path);
  if (IsDevToolsFileSystemAdded(GetDevToolsWebContents(), path.AsUTF8Unsafe()))
    return;
  FileSystem file_system = CreateFileSystemStruct(
      GetDevToolsWebContents(), file_system_id, path.AsUTF8Unsafe(), type);
  std::unique_ptr<base::DictionaryValue> file_system_value(
      CreateFileSystemValue(file_system));
  auto* pref_service = GetPrefService(GetDevToolsWebContents());
  DictionaryPrefUpdate update(pref_service, prefs::kDevToolsFileSystemPaths);
  update.Get()->SetWithoutPathExpansion(path.AsUTF8Unsafe(),
                                        std::make_unique<base::Value>(type));
  inspectable_ontents_->CallClientFunction(
      "DevToolsAPI.fileSystemAdded", nullptr, file_system_value.get(), nullptr);
}
void WebContents::DevToolsRemoveFileSystem(