How can PHP functions be utilized to change variable values on click events in a PHP forum thread?

To change variable values on click events in a PHP forum thread, you can use JavaScript to trigger AJAX requests to update the variables in the backend PHP script. The PHP script can handle the request, update the variable values, and return the updated values to the frontend for display.

```php
// PHP script to handle AJAX request and update variable values
if(isset($_POST['variable_value'])) {
    $new_value = $_POST['variable_value'];
    
    // Update the variable values based on the new value
    // Example: $_SESSION['variable'] = $new_value;
    
    // Return the updated variable values
    echo json_encode(array('status' => 'success', 'new_value' => $new_value));
}
```
Make sure to include this PHP script in your forum thread page and have corresponding JavaScript code to trigger the AJAX request on click events.