For every missing provision, push that provision onto an array, forcing the passenger to consider the item:

sub check_required_items {
  my $who = shift;
  my $items = shift;
  my @required = qw(preserver sunscreen water_bottle jacket);
  my @missing = ( );

  for my $item (@required) {
    unless (grep $item eq $_, @$items) { # not found in list?
      print "$who is missing $item.\n";
      push @missing, $item;
    }
  }

  if (@missing) {
    print "Adding @missing to @$items for $who.\n";
    push @$items, @missing;
  }
}

Note the addition of the @missing array. If you find any items missing during the scan, push them into @missing. If there's anything there at the end of the scan, add it to the original provision list.