Hi Cameron -- Probably the best resource for that is here which briefly discusses the raw customers/get API call. However, you might consider using this method for checking status.

Determining whether or not a customer is canceled via the API is usually left up to a wrapper. Here's the relevant methods of the PHP wrapper (CheddarGetter_Response):

/**
 * Whether or not a customer's subscription is active and in good standing
 *
 * @param $code string your code for the customer - required if more than one customer is in the response
 * @param $remainActiveThroughEndOfPeriod bool Set to true if you'd like the account to remain active until the end of the current payment period rather than inactive at the moment of cancelation
 * @throws CheddarGetter_Response_Exception if the response type is incompatible or if a $code is not provided and the response contains more than one customer
 * @return array
 */
public function getCustomerIsActive($code = null, $remainActiveThroughEndOfPeriod = false) {
    $subscription = $this->getCustomerSubscription($code);
    if ($subscription['canceledDatetime']) {
        if (strtotime($subscription['canceledDatetime']) <= time()) {
            if ($remainActiveThroughEndOfPeriod) {
                $invoice = $this->getCustomerInvoice($code);
                if (strtotime($invoice['billingDatetime']) > time()) {
                    return true;
                }
            }
            return false;
        }
    }
    return true;
}

/**
 * Is this customer's account pending paypal preapproval confirmation?
 *
 * @param $code string your code for the customer - required if more than one customer is in the response
 * @throws CheddarGetter_Response_Exception if the response type is incompatible or if a $code is not provided and the response contains more than one customer
 * @return array
 */
public function getCustomerIsWaitingForPayPal($code = null) {
    $subscription = $this->getCustomerSubscription($code);
    if (
        $subscription['canceledDatetime']
        && strtotime($subscription['canceledDatetime']) <= time()
        && $subscription['cancelType'] == 'paypal-wait'
    ) {
        return true;
    }
    return false;
}