The state machine example is a good one. It's a textbook case of unreachable code.
The null-checking example is not good. If the external API returns a null where you don't expect one, UnreachableException will be thrown. It doesn't matter if the documentation says it will never be null; clearly the code isn't unreachable. All you need to reach it is bad data! (InvalidDataException would be a better choice, though arguably not an ideal one.)
If you can write a unit test that makes your code throw UnreachableException, you almost certainly should be throwing a different exception.
The null-checking example is not good. If the external API returns a null where you don't expect one, UnreachableException will be thrown. It doesn't matter if the documentation says it will never be null; clearly the code isn't unreachable. All you need to reach it is bad data! (InvalidDataException would be a better choice, though arguably not an ideal one.)
If you can write a unit test that makes your code throw UnreachableException, you almost certainly should be throwing a different exception.