Does AJAX loaded content get a "document.ready"?

Javascript in the resulting ajax call will not be excecuted (by default) due to safety. Also, you can't directly bind event to non-existing elements.
You can bind an event to some parent that does exist, and tell it to check it's children:

$(document).ready(function(){
    $(document).on('eventName', '#nonExistingElement', function(){ alert(1); }
    // or:
    $('#existingParent').on('eventName', '#nonExistingElement', function(){ alert(1); }
});

Always try to get as close to the triggering element as you can, this will prevent unnessesary bubbling through the DOM

---

If you have some weird functions going on, you could do something like this:

function bindAllDocReadyThings(){
    $('#nonExistingElement').off().on('eventName', function(){ alert(1); }
    // Note the .off() this time, it removes all other events to set them again
}
$(document).ready(function(){
    bindAllDocReadyThings();
});
$.ajaxComplete(function(){
    bindAllDocReadyThings();
});

To answer your question: No, document.ready will not fire again once a ajax request is completed. (The content in the ajax is loaded into your document, so there isn't a second document for the ajax content).

To solve your problem just add the event listener to the Element where you load the ajax content into it. For example:

$( "div.ajaxcontent-container" ).on( "click", "#id-of-the-element-in-the-ajax-content", function() {
  console.log($( this ));
});

For #id-of-the-element-in-the-ajax-content you can use any selector you would use in $("selector"). The only difference is, only elements under div.ajaxcontent-container will be selected.

How it works: As long as div.ajaxcontent-container exists all elements (if they exist now or only in the future) that match the selector #id-of-the-element-in-the-ajax-content will trigger this click-event.

try this, that is not working because your control is not yet created and you are trying to attach a event, if you use on event it will work fine. let me know if you face any issues.

$(document).ready(function(){
    $(document).on('click', '#element', function (evt) {
        alert($(this).val());
    });
});

The answer here is a delegated event:

JSFiddle

JSFiddle - Truly dynamic

jQuery

$(document).ready(function(){
    // Listen for a button within .container to get clicked because .container is not dynamic
    $('.container').on('click', 'input[type="button"]', function(){
        alert($(this).val());
    });

    // we bound the click listener to .container child elements so any buttons inside of it get noticed
    $('.container').append('<input type="button" class="dynamically_added" value="button2">');
    $('.container').append('<input type="button" class="dynamically_added" value="button3">');
    $('.container').append('<input type="button" class="dynamically_added" value="button4">');
    $('.container').append('<input type="button" class="dynamically_added" value="button5">');
});

HTML

<div class="container">
    <input type="button" class="dynamically_added" value="button1">
</div>