Each method of mysqli can fail. Luckily, nowadays mysqli can report every problem to you, all you need is ask. Simply add this single line to the connection code,
mysqli_report(MYSQLI_REPORT_ERROR | MYSQLI_REPORT_STRICT);
And after that every error will reveal itself. No need to test any return values ever, just write your statements right away:
$stmt = $mysqli->prepare("INSERT INTO testtable VALUES (?,?,?)");
$stmt->bind_param('iii', $x, $y, $z);
$stmt->execute();
When the error occurs at any step, it will throw a usual PHP Exception that can be handled or just reported the same way as any other PHP error. Just make sure you configured PHP error reporting properly, i.e. on the dev server errors are displayed on-screen and on the production server errors are never displayed but logged instead.