### 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
content::WebContents* source,
    const content::NativeWebKeyboardEvent& event) {
  if (event.GetType() == blink::WebInputEvent::Type::kRawKeyDown ||
      event.GetType() == blink::WebInputEvent::Type::kKeyUp) {
    bool prevent_default = Emit("before-input-event", event);
    if (prevent_default) {
      return content::KeyboardEventProcessingResult::HANDLED;
    }
  }
  return content::KeyboardEventProcessingResult::NOT_HANDLED;
}
void WebContents::ContentsZoomChange(bool zoom_in) {
  Emit("zoom-changed", zoom_in ? "in" : "out");
}
void WebContents::EnterFullscreenModeForTab(
    content::RenderFrameHost* requesting_frame,
    const blink::mojom::FullscreenOptions& options) {
  auto* source = content::WebContents::FromRenderFrameHost(requesting_frame);
  auto* permission_helper =
      WebContentsPermissionHelper::FromWebContents(source);
  auto callback =
      base::BindRepeating(&WebContents::OnEnterFullscreenModeForTab,
                          base::Unretained(this), requesting_frame, options);
  permission_helper->RequestFullscreenPermission(callback);
}
void WebContents::OnEnterFullscreenModeForTab(