MutationObserver vs DOMSubtreeModified example which allows detecting changes in elements that don't exist yet, by detecting changes in a parent element that does exist at the time the function is executed.

MutationObserverVsDOMSubtreeModified.js

// This example depends on jQuery().on and _.debounce

// Create a MutationObserver to trigger a callback function
// when the element located via document.querySelector(elementSelector) changes
function getMutationObserver(elementSelector, callback) {
	var observer = new MutationObserver(callback);
	var config = { attributes: true, childList: true, characterData: false };
	observer.observe(document.querySelector(elementSelector), config);

	return observer;
}

function onFieldRenderedAndChanged(parentSelector, fieldSelector, callback) {
	var observer;
	// observe changes to the 'parentSelector' element
	observer = getMutationObserver(parentSelector, function(mutations) {				
		// If the 'fieldSelector' element exists in the DOM
		if(!!document.querySelector(fieldSelector)) {
			// Disconnect parent element mutation observer
			observer.disconnect();

			// Wait for 'fieldSelector' taxonomy field to update, trigger callback when it does
			getMutationObserver(parentSelector + " " + fieldSelector, callback);
		}
	});
}

// callback function to be executed when the element retrievable via
// the 'fieldSelector' CSS selector changes
function onFieldChangedCallback(fieldSelector) {
	var field = document.querySelector(fieldSelector);
	// do something with updated field element here
}

// CSS selector for an element that exists on the page when this JavaScript is executed,
// which is a parent of the element referenced by 'fieldSelector'.
var parentSelector = ".parentElementClass";

// CSS selector for element which does not exist on the page when this JavaScript is executed,
// which is a child of the element referenced by 'parentSelector'.
var fieldSelector = ".childElementClass";

// Use MutationObserver if available or fallback to DOMSubtreeModified in older browsers.
// Rate-limit event handling with _.debounce to reduce performance impact.
if (MutationObserver) {
	onFieldRenderedAndChanged(parentSelector, fieldSelector, _.debounce(onFieldChangedCallback.bind(this, fieldSelector), 500));					
}
else {
	$(parentSelector).on("DOMSubtreeModified", fieldSelector, _.debounce(onFieldChangedCallback.bind(this, fieldSelector), 500));
}