### 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
#include "shell/browser/api/electron_api_ontents.h"
#include <limits>
#include <memory>
#include <set>
#include <string>
#include <unordered_set>
#include <utility>
#include <vector>
#include "base/containers/id_map.h"
#include "base/files/file_util.h"
#include "base/json/json_reader.h"
#include "base/no_destructor.h"
#include "base/optional.h"
#include "base/strings/utf_string_conversions.h"
#include "base/task/current_thread.h"
#include "base/task/post_task.h"
#include "base/task/thread_pool.h"
#include "base/threading/scoped_blocking_call.h"
#include "base/threading/sequenced_task_runner_handle.h"
#include "base/threading/thread_restrictions.h"
#include "base/threading/thread_task_runner_handle.h"
#include "base/values.h"
#include "chrome/browser/browser_process.h"
#include "chrome/browser/ssl/security_state_tab_helper.h"
#include "chrome/browser/ui/views/eye_dropper/eye_dropper.h"
#include "chrome/common/pref_names.h"
#include "components/prefs/pref_service.h"
#include "components/prefs/scoped_user_pref_update.h"
#include "components/security_state/content/content_utils.h"