### 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
if (!IsDevToolsFileSystemAdded(GetDevToolsWebContents(), file_system_path)) {
    OnDevToolsIndexingDone(request_id, file_system_path);
    return;
  }
  if (devtools_indexing_jobs_.count(request_id) != 0)
    return;
  std::vector<std::string> excluded_folders;
  std::unique_ptr<base::Value> parsed_excluded_folders =
      base::JSONReader::ReadDeprecated(excluded_folders_message);
  if (parsed_excluded_folders && parsed_excluded_folders->is_list()) {
    for (const base::Value& folder_path : parsed_excluded_folders->GetList()) {
      if (folder_path.is_string())
        excluded_folders.push_back(folder_path.GetString());
    }
  }
  devtools_indexing_jobs_[request_id] =
      scoped_refptr<DevToolsFileSystemIndexer::FileSystemIndexingJob>(
          devtools_file_system_indexer_->IndexPath(
              file_system_path, excluded_folders,
              base::BindRepeating(
                  &WebContents::OnDevToolsIndexingWorkCalculated,
                  weak_factory_.GetWeakPtr(), request_id, file_system_path),
              base::BindRepeating(&WebContents::OnDevToolsIndexingWorked,
                                  weak_factory_.GetWeakPtr(), request_id,
                                  file_system_path),
              base::BindRepeating(&WebContents::OnDevToolsIndexingDone,
                                  weak_factory_.GetWeakPtr(), request_id,
                                  file_system_path)));
}
void WebContents::DevToolsStopIndexing(int request_id) {