To complement on @vararis's answer:

Select2 attached to a <select> element does not allow for custom createSearchChoice nor query functions, hence we will need to manually add an option element (I'll add it as the last option of the element so we can easily .pop it out of the results set):

<select>

  ...

  <option value=0>Other</option>

</select>

Then pass a custom matcher function so that this Other option is always matched.

NOTE: Select2 3.4+ uses a different default matcher than the one currently shown in the documentation, this new one has a call to the stripDiacritics function so that a matches á for instance. Therefore I'll apply the default matcher that comes with the Select2 version included in the page to apply its default matching algorithm to any option that's not the Other option:

matcher: function(term, text) {

  return text==='Other' || $.fn.select2.defaults.matcher.apply(this, arguments);

},

Finally, we need to remove the Other option from the results set when there's any result besides the Other result (which is initially always in the results set):

sortResults: function(results) {

  if (results.length > 1) results.pop();

  return results;

}

Demo