Проблема решена.
<form action="php/post_delete.php" method="post">
<input type = "text" name = "id" value ="' .$result['id']. '" hidden />
<input type="submit" value="Удалить"><br>
</form>';
...и
<?php
$id = $_POST['id'];
$query = database::query("DELETE FROM punk WHERE id = '$id'");
?>