Can the inner class with private constructor be extended?

Yes.

package org.javatutorials.accessModifer.protectedPackage;

public class PrivateConstructorInnerClass {

	   class Parent {
	        private Parent() {
	            System.out.println("Hello from Parent");
	        }
	    }

	     class Child extends Parent {
	        public Child() {
	        	System.out.println("Hello from Child");
	        }
	    }

	    public static void main(String[] str) {
	       PrivateConstructorInnerClass pc = new PrivateConstructorInnerClass();
	       pc.new Child();
	    }
}

Output:

Hello from Parent
Hello from Child

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