Hello, Tiff_1984.
Thank you for contributing to Apple Support Communities.
We were sorry to read about the issues you're experiencing with your iPhone 11, and we'd like to see if we can help you find a resolution to your unexpected shutdowns. If we understand correctly, when your iPhone becomes unresponsive you're not able to get it to force restart, and eventually the device shuts down.
In this case, we highly recommend following the guidance in this article:
If your iOS or iPadOS device restarts or displays the Apple logo or a spinning gear unexpectedly - Apple Support
- Make sure that your iOS software is updated.
- Check the Battery Health screen to see if your battery is impacting the performance on your iPhone.
Cheers.