Can a SerializedProperty have a null value in a CustomPropertyDrawer?

So, suppose I have a custom serializable class like this:

[System.Serializable]
public class MyClass {
 public string someField, someOtherField; // just an example
} // note it's a class, not struct

And use it in a script:

public class MyScript : MonoBehaviour {
 public MyClass testField = null;
 public MyClass[] testArray = { null, new MyClass() };
} // note I want to differentiate null from empty instance

And I am making a custom property drawer for it:

[CustomPropertyDrawer(typeof(MyClass), true)] // true, because will have subclasses
public class MyClassDrawer : PropertyDrawer {
 public override void OnGUI(Rect position, SerializedProperty property, GUIContent label) {
  // property never seems to be null...
  // also tried this:
  var obj = base.fieldInfo.GetValue(property.serializedObject.targetObject);
  Debug.Log(obj); // MyClass | MyClass[]
  Debug.Log(obj==null); // False
 }
}

How can I know when this property has a value of null, instead of empty?

I want to make a drawer which differentiates null (none) from instance with empty fields. I want to be able to set null in the inspector, or set a value if desired.

Is there a way to do this without changing implementation of MyClass?

Does the serialization accept null values even if you don't extend UnityEngine.Object (I would prefer to avoid that)?