[evilduck]

The article isn't stellar about explaining what they mean. FaceID and TouchID as implemented by Apple requires you to type in your password every couple of days to ensure you don't forget it. They augment your password (and weaken overall security) but they don't replace your password. I can't speak to every similar Android and Windows implementations, but I charitably assume they've followed the same path, Google Pixels have at least.

So to answer your question specifically for an iPhone, if you're using FaceID and get in a face-mangling accident, you type in your password until your face heal enough to stop changing and then set up FaceID again with your new mug.