It’s because you’ve removed the id which is how you’re finding the element. This line of code is trying to add id="page_navigation1" to an element with the id named page_navigation1, but it doesn’t exist (because you deleted the attribute):
$("#page_navigation1").attr("id","page_navigation1");
Demo: 
If you want to add and remove a class that makes your <div> red use:
$( '#page_navigation1' ).addClass( 'red-class' );
And:
$( '#page_navigation1' ).removeClass( 'red-class' );
Where red-class is:
.red-class {
background-color: red;
}