It is my understanding that in C++ objects of derived classes invoke the derived class' constructor but before the body is executed the base class' constructor is invoked and takes effect and then the derived class' constructor's body is executed. If this knowledge is correct, then what happens if the base class' constructor initializes a private variable of the base class that would not be inherited to the derived class, when a new objecct of the derived class is declared.
The variable still exists. You'd have to provide a means of access to it either via protected or public mechanisms, or means of altering it from a function declared in the base class that allows you to do so. The access restrictions obviously still apply.