I downvoted the OP (belatedly). Here's why:

"Among other expressions, I have tried: m/subsid(.*)(">)/" ... and not even in code tags, at that.

Missing from your regex: modifiers to make it case-insentive and multi-line... and context (even if simplified) to make it easy for us to spot non-regex errors.

The code in your narrative doesn't even come close to doing what you say you want. It's time for you to do some reading -- in this case, perlretut and friends -- and stop typing in poorly constructed questions every time you face an issue.

Also, you've posted too much data: if you've stated your intention precisely, then there's no need for the entire html for Row 9 of the table. This is a very poor post, even given the low quality of your recent nodes.

So here's a crummy example (see much better suggestions above re modules) constructed solely to demonstrate that if you're going down the (fool's) path of trying to parse html with a regex, it can be done. It's so bad an example that I feel free to offer it to a gimmé-artist:

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

my @lines = <DATA>;
for my $line(@lines) {
    print "| $line |";
    if ($line =~ /(<a href.+<\/a>)/) {  # note, no need to capture the
+ whole of row 9
           print "$1 \n\n";
    }
    else { 
         print "Crummy regex\n"
    }
}

__DATA__
<td scope="row">9</td>
             <td scope="row">SUBSIDIARIES OF THE REGISTRANT</td>
             <td scope="row"><a href="/Archives/edgar/data/1050122/000
+092735601000365/0000927356-01-000365-0009.txt">0009.txt</a></td>
             <td scope="row">EX-21.1</td></>

And here's execution:

<c>C:>wrkrbeejunk.pl
| <td scope="row">9</td>
 |Crummy regex
|              <td scope="row">SUBSIDIARIES OF THE REGISTRANT</td>
 |Crummy regex
|              <td scope="row"><a href="/Archives/edgar/data/1050122/0
+00092735601000365/0000927356-01-000365-0009.txt">0009.txt</a></td>
 |<a href="/Archives/edgar/data/1050122/000092735601000365/0000927356-
+01-000365-0009.txt">0009.txt</a>

|              <td scope="row">EX-21.1</td> |Crummy regex

C:\>
[download]