01_non_stable_sort.php

<?php
$list = [];
$keys = ['a', 'x'];

foreach ($keys as $key) {
	$list[] = ['key' => $key, 'quality' => 1];
}

array_walk($list, function (&$v, $k) {
	// Decorate
	$v['quality'] = [$v['quality'], $k];
});

usort($list, function ($a, $b) {
	return strcmp($a['quality'], $b['quality']);
});

array_walk($list, function (&$v, $k) {
	// Undecorate
	$v['quality'] = $v['quality'][0];
});

var_dump($list);

02_actual_output.txt

array(2) {
  [0] =>
  array(2) {
    'key' =>
    string(1) "x"
    'quality' =>
    int(1)
  }
  [1] =>
  array(2) {
    'key' =>
    string(1) "a"
    'quality' =>
    int(1)
  }
}

03_expected_output.txt

array(2) {
  [0] =>
  array(2) {
    'key' =>
    string(1) "a"
    'quality' =>
    int(1)
  }
  [1] =>
  array(2) {
    'key' =>
    string(1) "x"
    'quality' =>
    int(1)
  }
}