...cannot trust the files to be in sequence, but
they will be in order, the gap will be unspecific

Woah! That really throws a monkey wrench in things. So the file 9999 might not even exist, but 9998 and 0000 will? Hrmm....this calls for another solution. Let's have the program make a best guess as to where the selection of files actually begins. First, some code to generate "random elmos" (but not infinite elmos!):

my ($rand,%seen,@files);
my $number=shift || 15;
{
  $rand = substr(rand,-7,4);
  unless ($seen{$rand}++) { ## Files must be unique!
    push @files, "elmo$rand.txt";
    --$number or last;
  }
  redo;
}
[download]

And here's the actual code. Globbing is a better way for actual use, of course.

my @files = <elmo*.txt>;

## Convert the list to numbers and warn about any unusual elmos:
@files = map {
  m/^elmo(\d{4})\.txt$/ and $1 or 
  die "What is $_ doing here?!\n"; } @files;

## Now figure out where the largest gap is:
my ($diff,$old,$high);
for (sort @files) {
  $diff=$_-$old and $high=$_ if $_-$old>$diff;
  $old=$_;
}

## Now go in order, starting at the first value after the gap:
for (
  map  {$_->[0]}
  sort {$a->[1] <=> $b->[1] }
  map  {[$_, $_ >= $high ? $_-10000 : $_]} @files) {
  print "Parsing elmo$_.txt\n";
}
[download]