a long option whose "val" happens to be `0`?

From GNU C library manual

#include <stdio.h>
#include <stdlib.h>
#include <getopt.h>

/* Flag set by ‘--verbose’. */
static int verbose_flag;

int
main (int argc, char **argv)
{
  int c;

  while (1)
    {
      static struct option long_options[] =
        {
          /* These options set a flag. */
          {"verbose", no_argument,       &verbose_flag, 1},
          {"brief",   no_argument,       &verbose_flag, 0},
          /* These options don’t set a flag.
             We distinguish them by their indices. */
          {"add",     no_argument,       0, 'a'},
          {"append",  no_argument,       0, 'b'},
          {"delete",  required_argument, 0, 'd'},
          {"create",  required_argument, 0, 'c'},
          {"file",    required_argument, 0, 'f'},
          {0, 0, 0, 0}
        };
      /* getopt_long stores the option index here. */
      int option_index = 0;

      c = getopt_long (argc, argv, "abc:d:f:",
                       long_options, &option_index);

      /* Detect the end of the options. */
      if (c == -1)
        break;

      switch (c)
        {
        case 0:
          /* If this option set a flag, do nothing else now. */
          if (long_options[option_index].flag != 0)
            break;
          printf ("option %s", long_options[option_index].name);
          if (optarg)
            printf (" with arg %s", optarg);
          printf ("\n");
          break;

        case 'a':
          puts ("option -a\n");
          break;

What kind of option will make the program reach inside case 0 and

printf("option %s", long_options[option_index].name);

Is it a long option whose flag is not set, or a long option whose "val" happens to be 0?

What kind of option does " {0, 0, 0, 0}" specify?