For... reasons I was working with bad data and a migration into Drupal 8 had me in a situation where I couldn't trust that the source file URL was actually present. The following is a migration process plugin that will check the URL and skip the row if it is a 404.

SkipOn404.php

<?php

namespace Drupal\migrate_custom\Plugin\migrate\process;

use Drupal\migrate\ProcessPluginBase;
use Drupal\migrate\MigrateExecutableInterface;
use Drupal\migrate\MigrateSkipRowException;
use Drupal\migrate\Row;
use Drupal\Component\Utility\UrlHelper;

/**
 * Provides a process plugin that checks if a URL is a 404 and skips the row if so.
 *
 * @MigrateProcessPlugin(
 *  id = "skip_on_404"
 * )
 */
class SkipOn404 extends ProcessPluginBase {

  /**
   * Stops processing the current property when value is not set.
   *
   * @param mixed $value
   *   The input value. If an array the first item is assumed to be the URL we are checking.
   * @param \Drupal\migrate\MigrateExecutableInterface $migrate_executable
   *   The migration in which this process is being executed.
   * @param \Drupal\migrate\Row $row
   *   The row from the source to process.
   * @param string $destination_property
   *   The destination property currently worked on. This is only used together
   *   with the $row above.
   *
   * @return mixed
   *   The input value, $value, if the test was not a 404.
   *
   * @throws \Drupal\migrate\MigrateSkipRowException
   *   Thrown if the source property is not set and the row should be skipped,
   *   records with STATUS_IGNORED status in the map.
   */
  public function row($value, MigrateExecutableInterface $migrate_executable, Row $row, $destination_property) {
    if (is_array($value)) {
      $url = $value[0];
    }
    else {
      $url = $value;
    }
    if (!UrlHelper::isValid($url, TRUE)) {
      $message = !empty($this->configuration['message']) ? $this->configuration['message'] : 'SkipOn404: invalid URL';
      throw new MigrateSkipRowException($message);
    }

    $handle = curl_init($url);
    curl_setopt($handle,  CURLOPT_RETURNTRANSFER, TRUE);
    $response = curl_exec($handle);
    $http_code = curl_getinfo($handle, CURLINFO_HTTP_CODE);

    if ($http_code == 404) {
      $message = !empty($this->configuration['message']) ? $this->configuration['message'] : 'SkipOn404: ' . $url;
      throw new MigrateSkipRowException($message);
    }
    return $value;
  }
}