Privacy mode is designed for when someone is at the property, not for when everyone has left. This mode disables the keypad and if it's offline you won't be able to use the app to unlock the door.
You can try restarting your Nest Connect and/or Wifi router if you're able to control those remotely. If that doesn't work and nobody is inside the property to unlock the door, you'll need to call a locksmith unfortunately.
