Here are few example of how to using it.

The first is basic example.

<?php
$file = __DIR__ . '/text.txt';

if (is_file($file) && is_writable($file)) {
    @unlink($file);
    echo '<small style="color: #ccc;">' . $file . ' was deleted.</small><br>' . PHP_EOL;
}

echo '<p>Calling to <code>fastcgi_finish_request()</code>.</p>' . PHP_EOL;

echo '<p>If success, the file ' . $file . ' will be created.</p>' . PHP_EOL;

if (function_exists('fastcgi_finish_request')) {
    fastcgi_finish_request();
} else {
    echo '<p style="color: red;">This server does not support <code>fastcgi_finish_request()</code> function.</p>' . PHP_EOL;
    echo 'Exit now.<br>' . PHP_EOL;
    exit();
}

echo 'This line will be not echo out.<br>' . PHP_EOL;

file_put_contents($file, date('Y-m-d H:i:s') . PHP_EOL, FILE_APPEND);
?>

The file text.txt will be create if successfully.

==========================

The second is about execution timeout.

<?php
set_time_limit(5);

$file = __DIR__ . '/text.txt';

if (is_file($file) && is_writable($file)) {
    @unlink($file);
    echo '<small style="color: #ccc;">' . $file . ' was deleted.</small><br>' . PHP_EOL;
}

echo '<p>Testing timeout and <code>fastcgi_finish_request()</code> function.</p>' . PHP_EOL;

echo '<p>Set timeout to ' . ini_get('max_execution_time') . ' seconds.</p>' . PHP_EOL;

echo '<p>Calling to <code>fastcgi_finish_request()</code>.</p>' . PHP_EOL;

echo '<p>If success, the file ' . $file . ' will be created but error will be shown in the log.</p>' . PHP_EOL;

if (function_exists('fastcgi_finish_request')) {
    fastcgi_finish_request();
} else {
    echo '<p style="color: red;">This server does not support <code>fastcgi_finish_request()</code> function.</p>' . PHP_EOL;
    echo 'Exit now.<br>' . PHP_EOL;
    exit();
}

$i = 1;
while(true){
    if ($i <= 10) {
        file_put_contents($file, date('Y-m-d H:i:s') . PHP_EOL, FILE_APPEND);
        $i++;
    }
    //to infinity and beyond...
}
?>

I found that the code will be working as long as it is not reach timeout setting in php.ini or set_time_limit() function.