How does \Magento\Sales\Model\ResourceModel\Order\Handler\State::check() work?

Context: How does an order saving work?

958164/app/code/Magento/Sales/Model/ResourceModel/Order/Handler/State.php#L16-L49

class State
{
    /**
     * Check order status before save
     *
     * @param Order $order
     * @return $this
     * @SuppressWarnings(PHPMD.CyclomaticComplexity)
     * @SuppressWarnings(PHPMD.NPathComplexity)
     */
    public function check(Order $order)
    {
        if (!$order->getId()) {
            return $order;
        }
        if (!$order->isCanceled() && !$order->canUnhold() && !$order->canInvoice() && !$order->canShip()) {
            if (0 == $order->getBaseGrandTotal() || $order->canCreditmemo()) {
                if ($order->getState() !== Order::STATE_COMPLETE) {
                    $order->setState(Order::STATE_COMPLETE)
                        ->setStatus($order->getConfig()->getStateDefaultStatus(Order::STATE_COMPLETE));
                }
            } elseif (floatval($order->getTotalRefunded())
                || !$order->getTotalRefunded() && $order->hasForcedCanCreditmemo()
            ) {
                if ($order->getState() !== Order::STATE_CLOSED) {
                    $order->setState(Order::STATE_CLOSED)
                        ->setStatus($order->getConfig()->getStateDefaultStatus(Order::STATE_CLOSED));
                }
            }
        }
        if ($order->getState() == Order::STATE_NEW && $order->getIsInProcess()) {
            $order->setState(Order::STATE_PROCESSING)
                ->setStatus($order->getConfig()->getStateDefaultStatus(Order::STATE_PROCESSING));
        }
        return $this;
    }
}

Details: