In case you are thinking it might be in the calling code, I used it exactly as the file handle example.

Not so friendly. I knocked together the following from your two posts:

#! perl -slw
use strict;
use List::Util 'first';

sub gen_merger {
    my( $list, $fetch, $compare, $finish ) = @_;
    my @item = map $fetch->($_), @$list;

    my $done;
    return sub {
        return $finish if $done;
        my $idx  = first{ $item[ $_ ] ne $finish } 0 .. $#item;
        my $next = $item[ $idx ];
        for( $idx + 1 .. $#item ) {
            next if $item[ $_ ] eq $finish;
            my $result = $compare->( $next, $item[$_] );
            #$next = $item[$_] if $result == 1;
            # Need to keep track of which one we use not just value

            ( $idx, $next ) = ( $_, $item[$_] ) if $result == 1;
        }
        $item[ $idx ] = $fetch->( $list->[ $idx ] );
        #$done = 1 if ! first {$item[$_] ne $finish} $idx .. $#item;
        # First element of array is 0 so use defined instead of truth
        $done = 1 if ! defined first {$item[$_] ne $finish} $idx .. $#
+item;
        return $next;
    };
}

my $finish   = 'A val that is guaranteed not to be present in any list
+';
my @list;

open $list[ $_-1 ], '<', "file$_" or die $! for 1 .. 9;

my $fetch    = sub {
    my $fh = shift @_;
    return $finish if eof $fh;
    return scalar <$fh>;
};

my $compare  = sub {
    my( $line1, $line2) = @_;
    my( $stamp1 ) = $line1 =~ /^(\d+)/;
    my( $stamp2 ) = $line2 =~ /^(\d+)/;
    return $stamp1 <=> $stamp2;
};

my $next = gen_merger( \@list, $fetch, $compare, $finish );

while( 1 ) {
    my $item = $next->();
    last if defined $item && $item eq $finish;
    printf "$item";
}
[download]

Gen'd 9 sorted files of 100,000 integers each, and merged them:  C:\test\890799>..\890799 >merged. The merge completed successfully and correctly and used a rock steady 3.1MB from start to finish.

There is something in your calling code that is different from your old post.