I have the Droid Incredible 2 and my Google Search Widget just disappeared from my home page when I restarted it. All my other apps and widgets are still there. I went back into the Widget list and I could not find an entry named "Google Search" or just "Search" although all the other Google apps/widgets were still there. It is also gone from the list of all my apps. However, when trying to uninstall apps, I see the "Google Search" app listed. Since it came preinstalled on the phone, I cannot uninstall it. Going to Google Search app page on the Android Market, it confirms that the app is installed, but I have no options to do anything. Is there any way I can get this app/widget back?
I'm sorry to hear that the widget is missing. That's unusual. I did research and found nothing related to this concern. I did confirm that the widget is named "Google Search". I would just reboot the phone again, then you should see the widget re-appear since it hasn't been removed at all.
Have you installed any other search engines on the phone? You can enable safe mode to see if the widget is listed then, if so then an app is likely causing the widget to be disabled. You know how to uninstall an application so I would remove any recently added apps.
I would also recommend going into Settings>Applications>Manage Apps>All>Google Search then check if defaults have been set up. If so, clear them out.
Please advise that the widget has working properly again!