Hello,
Compiled an old project with version 5.50 and noticed this : when the phone is rebooted an existing widget does not receive _Click events until the main Activity has been opened.
So, I have tried with an old apk and noticed that the widget was really restarted when the phone was rebooted. Now, but I could be wrong, I can see the widget started 3 times but no event seems to be fired (tested on Sony T3, Android 4.4.4 - compiled with android:minSdkVersion="8" android:targetSdkVersion="22", release (obfuscated))