Benefit of Generic Constructors

What is the benefit of having generic constructor for a non-generic class? Java spec permits the following:

class NonGeneric {
  <T> NonGeneric() { }
  ...
  NonGeneric ref = new <String> NonGeneric();
}

Can one come up with a realistic example of when it enhances the typesafety of the class? How would it be better than using Generic in the first place.

I understand that Java designers wanted the constructors to be more consistent with methods. Given that constructors can have side-effects, generic constructors can use generics to mutate some parameters whose references aren't retained, as in

<T> NonGeneric(T obj, List<T> list) {
  list.add(obj);
  // Don't hold a reference to list
}