Can jquery event delegation work with other javascript / jquery functions?

Question

I was trying add a check value function for further work, currently using jquery event delegation,

and the function would be according the value of #input-sample

such as if ($('#input-sample').val() <= 0)

But I don't know how to set the function work as expect.

---

lets say we had some input value, and some button like below:

<input id="input-sample" value="3"/>

<button class="btn btn-select">SELECT</button>
<button class="btn btn-select">SELECT</button>
<button class="btn btn-select">SELECT</button>

I create a function let the btn-select as able to click to do ajax request.

then let the $('#input-sample').val() updated each time.

$('.btn-select').click(function(e){
  e.preventDefault(); // stop click go to next page
  $.ajax({ 
    xxx, xxx, xxx, // some ajax
    success: function (response) {

    // **** BUT! I just update the '#input-value' 
    $('#input-sample').val(
      parseInt($('#input-sample').val() - 1)
    );
  });
});

---

After the $('#input-sample').val() was down to 0,

I would need the event delegation check it for other function.

But somehow the event delegation cannot trigger it.

---

I tried create other kinds of function like

$('#input-sample').change(function(){}); // no luck,
$('#input-sample').on('change', function(){}); // noluck,
$(document).on('change', '#input-sample', function(){}); // same no luck, 

Is there any other function would work after the value of the #input-sample changed ?