I think you are still a little caught up in the source of your data, and not considering it purely from a string processing perspective. From my reading, your goals are:

1. Determine the number of unique 4-character prefixes (n + 1, n == 3) within a list of strings.
2. For each prefix group, determine the longest possible string anchored at the string start common between all members of the group

If the second goal is incorrect (you've never stated it but it seems to pervade your solutions), your goal can be achieved very simply with:

#!/usr/bin/perl 
use strict;
use warnings;

my %files = ();
while (<DATA>) {
    if (/(.{4})/) {
        $files{$1} = 1;
    }
}
foreach my $prefix (keys %files) {
    print "$prefix*\n";
}

__DATA__
abcpwbln08
abcpwbln07
abcpwbnn10
abcpwbnn06
adesicln09
adesicln08
adesicln01
adesicnn05
[download]

If you want to keep the second goal, one way to accomplish your goal (TIMTOWTDI) would be to compare the new postfix with the existing solution for that prefix, and shorten that guess until it matches the to criterion:

!/usr/bin/perl 
use strict;
use warnings;

my %files = ();
while (<DATA>) {
    if (my ($prefix,$postfix) = /(.{4})(.*)/) {
        if (exists $files{$prefix}) {
            my $pattern = $files{$prefix};
            while (not $postfix =~ /^$pattern/) {
                $pattern =~ s/.$//;
            }
            $files{$prefix} = $pattern;
        } else {
            $files{$prefix} = $postfix;
        }
    }
}
foreach my $prefix (keys %files) {
    print "$prefix$files{$prefix}*\n";
}

__DATA__
abcpwbln08
abcpwbln07
abcpwbnn10
abcpwbnn06
adesicln09
adesicln08
adesicln01
adesicnn05
[download]