The only way in which a constructor can report an error is by throwing an exception.
The C++ standard has this to say (in Section 15.2 "Constructors and destructors" which is within Section 15 "Exception Handling"). [Note: I have not preserved font changes or emphasis in the quote]
1 As control passes from a throw-expression to a handler, destructors are invoked for all automatic objects constructed since the try block was entered. The automatic objects are destroyed in the reverse order of the completion of their construction.
2 An object that is partially constructed or partially destroyed will have destructors executed for all of its fully constructed subobjects, that is, for subobjects for which the constructor has completed execution and the destructor has not yet begun execution. Should a constructor for an element of an automatic array throw an exception, only the constructed elements of that array will be destroyed. If the object or array was allocated in a new-expression and the new-expression does not contain a new-placement, the deallocation function (3.7.3.2, 12.5) is called to free the storage occupied by the object; the deallocation function is chosen as specified in 5.3.4. If the object or array was allocated in a new- expression and the new-expression contains a new-placement, the storage occupied by the object is deallocated only if an appropriate placement operator delete is found, as specified in 5.3.4.
3 The process of calling destructors for automatic objects constructed on the path from a try …