Unfortunately I don't have the time to see what this is really about and to delve into your code in its entirety. I have a few general remarks that hopefully will help you anyway...

Update: eventually I checked the rules and I provide some minimal but complete working example here: 433664.

#!/usr/bin/perl
# Shuffles cards
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Always -yes: always!-

use strict;
use warnings;
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in all but most trivial code (e.g. one-liners). This does not address your specific issue, but applies to any issue...

@pack = (1, 2, 3, 4, 5, 6, 7, 8);

As a side note, since you use .. below, I can't see why you don't use it here too...

sub b {
    push(@pack, shift @pack);
}
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Hmmm, while occasionally it can be handy to have a sub manipulating some "global" data, parameter passing is generally a much better solution. It's what a function is for.

I suggest you read something about @_, e.g. perlsub.

sub i {
    my ($a, $b, $c, $d, $e, $f, $g, $h) = @pack;
    @pack = ($e, $a, $f, $b, $g, $c, $h, $d);
}

sub o {
    my ($a, $b, $c, $d, $e, $f, $g, $h) = @pack;
    @pack = ($a, $e, $b, $f, $c, $g, $d, $h);
}
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Ditto as above. But then you may also use slicing instead. In that case you may also "generate" the subscripts rather than hardcoding them, but I agree that in this case you wouldn't earn much and probably hardcoding them is the best choice...

Also, it is always recommended to avoid using $a and $b as general purpose variables. This can lead to confusion and gotchas (see perlvar).

sub parse {
  my ($string) = @_;
  print "\nParse $string: ";
  
  foreach $offset (0..(length($string)-1)) {
        $char = substr($string, $offset, 1);
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I think that most people here would write

for (string =~ /./g) { # ...
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or

for (split //, $string) { # ...
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instead. As a side note I would also have (a local()) $_ instead of $string and so I'd have

for (/./g) { # ...
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or

for (split //) { # ...
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respectively.

        if ($char =~ /b|i|o/) {
          print "bio ";
          &{$char};
        }
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Ouch!

• Using symrefs is a Very Bad Thing(TM). In some cases it is necessary, but then you must really know what you're doing. It may seem safe to you to do so in this case, but if you get used to use them where they're not really needed they're likely to eventually bite you in the neck!!
• In any case the &-form of sub call should not be used nowadays unless you know what you're doing. It most likely won't do what you think it does, see perlsub.

        elsif ($char =~ /\d/) {
            print "digit ";
#            foreach (1..$char) { &parse(substr($string, $offset+1)); 
+}
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Ditto as above. Also, apart that the line is commented out, do you really want to have 1..$char?!?

Update: never mind, there's nothing wrong a priori with 1..$char above, only you now have foreach (1..$char) but you use $offset as if it were the loop iterator, in the loop.

Well, I couldn't go past this point in your code in detail, but fundamentally it seems to me that the same cmts as above apply. I will look into the rules and maybe provide some minimal sample code as time permits. (But then I'm sure others will do!)