import java.io.*;

public class Soluton {
    public class A {
        protected A() { } //конструктор по-умолчанию
    }

    public class B extends A implements Serializable {
        public B() { }
    }

    public static void main(String[] args) throws IOException {

        Soluton sol = new Soluton();
        B b = sol.new B(); // если A, B static  и заменить на B b = new B()

        ByteArrayOutputStream arrayOutputStream = new ByteArrayOutputStream();
        ObjectOutputStream oos = new ObjectOutputStream(arrayOutputStream);

        oos.writeObject(b); //<-error java.io.NotSerializableException

    }
}

private void writeObject(ObjectOutputStream out) throws IOException {}