JSFiddle - React, Tailwind, and code Playground

HTML

<input type="checkbox" value="Bill" id="CAT_Custom_173676_0" name="CAT_Custom_173676" />Bill<br />
<input type="checkbox" value="Dan" id="CAT_Custom_173676_1" name="CAT_Custom_173676" />Dan<br />
<input type="checkbox" value="Francis" id="CAT_Custom_173676_2" name="CAT_Custom_173676" />Francis<br />
<input type="text" class="cat_textbox" id="CAT_Custom_172786" name="CAT_Custom_172786" maxlength="1024"  />

JavaScript

$("input[type=checkbox]").change(function () {
    var newArr = $("input:checked").map(function () { return this.value; });
    $("#CAT_Custom_172786").val(newArr.get().join(","));
});