Given the evidence you've shown (some examples where the markup comes out right as well as a case where it's wrong because of a missing close tag), I think there's sufficient cause to to assume that, even without an "official" DTD, you can figure out where to put the close tag. (The nature of the XML generation bug appears to be constrained in a way that allows a "heuristic, speculative" solution to do the right thing.)

So here's how I would do it: read through the file one tag at a time (set the input-record-separator to ">"), maintain a stack of the open tags as they occur, pop them off the stack as their corresponding close-tags appear, and fill in missing close-tags where necessary.

(This way of reading might be noticeably inefficient on large data sets, and there are ways to chunk through the data with fewer iterations on the diamond operator; but see if it works well enough before thinking about optimizing it.)

#!/usr/bin/perl

use strict;
use warnings;

$/ = '>';   # read up to the end of one tag at a time

my $lineno = 0;
my @tagstack;

while (<>) 
{
    $lineno += tr/\n//;
    unless ( />$/ ) {  # must be at eof;
        print;
        next;
    }

    my ( $pre, $tag ) = ( /([^<]*)(<[^>]+?)>/ );

    if ( !defined( $tag )) {
        warn "'>' without prior '<' at or near line $lineno\n";
        print;
    }
    elsif ( $tag =~ m{^</} ) { # close tag: look for its open tag on t
+he stack
        unless ( @tagstack ) {
            warn "extra close tag '$tag' at or near line $lineno\n";
            print;
            next;
        }
        $tag = substr $tag, 2;
        my $stackindx = $#tagstack;
        while ( $stackindx >= 0 and $tagstack[$stackindx] ne $tag ) {
            $stackindx--;
        }
        if ( $stackindx < 0 ) {
            warn "close tag '$tag' lacks open tag at or near line $lin
+eno\n";
            print;
            next;
        }
        print $pre;
        if ( $stackindx != $#tagstack ) {  # add close tags as needed
            while ( $stackindx < $#tagstack ) {
                warn "added '</$tagstack[$#tagstack]>' at line $lineno
+\n";
                printf "</%s>\n", pop @tagstack;
                $lineno++;
            }
        }
        print "</$tag>";
        pop @tagstack;
    }
    elsif ( $tag =~ m{^<!} or $tag =~ m{/$} ) {  # "comment" or empty 
+tag
        print;
    }
    else {  # this must be an open tag -- push it on the stack
        $tag =~ s/<(\S+).*/$1/s;
        push @tagstack, $tag;
        print;
    }
}
[download]

I tested this on the examples you gave -- the good ones came out unaltered, and the bad one had the close-tag added where needed.

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