If you previously downloaded a file before (like a huge web log), and just want to get the remaining portion, do this:
$local_file_size = filesize($local_file_path);
$get_result = ftp_get($conn_id, $local_file_path, $remote_file_path, FTP_BINARY, $local_file_size);
This same code works regardless of wether the local file exists already or not. You should first test to make sure the local file is not bigger than the remote file.