Should a Singleton class be allowed to have children? Should we seal it? What are the pro's and con's?

For being able to inherit from a Singleton class, we would have to make the constructor protected instead of private. Now, that will be fine in c#, but the protected word in java gives both child-classes and package-classes access to the constructor. Which means not only classes that inherit from our Singleton can access the constructor but other classes in the same package can do it.

I'm a bit confused about all this facts. Maybe I am making a big fuss about nothing to worry about too much? Until now, I never had any necessity of trying to inherit from a Singleton, so maybe this is just an academic question!

Thanks