I know that ... some other module might have easier way to do this. But for now, I want to learn and apply HTML::Parser and regex ...

Ok, so you're committed to drilling all those holes in your head just to prove to yourself for sure that drilling holes in your head is a bad idea. Here's one approach:

c:\@Work\Perl\monks>perl -wMstrict -le
"use warnings;
 use strict;
 ;;
 use Regexp::Common;
 ;;
 use Data::Dump qw(dd);
 ;;
 my @lines = (
   'Summary</h1><table border=\"1\"><tr><th>Employee John Doe</th><th>
+-0.82</th>',
   'Summary</h1><table border=\"1\"><tr><th> Employee Fred D. Poe </th
+><th> -5.03 </th>',
   'Summary</h1><table border=\"1\"><tr><th>Employee Billy-Bob Toe</th
+><th> </th>',
   'Summary</h1><table border=\"1\"><tr><th>Employee</th><th>999</th>'
+,
   '<th>Employee  Prince  </th><th> 123</th>',
   '<th>Employee O</th><th> 1.23 </th>',
   );
 ;;
 my $rx_name = qr{ \S+? (?: \s+ \S+)*? }xms;
 my $rx_th_open  = qr{ \s* <   th > \s* }xms;
 my $rx_th_close = qr{ \s* < / th > \s* }xms;
 ;;
 my %per_employee;
 ;;
 LINE:
 for my $line (@lines) {
   my $parsed =
   my ($name, $amount) = $line =~ m{
     $rx_th_open Employee \s+ ($rx_name) $rx_th_close
     $rx_th_open ($RE{num}{real})?       $rx_th_close
     }xms;
   ;;
   if (not $parsed) {
     warn qq{'$line' failed to parse};
     next LINE;
     }
   ;;
   $amount = 'no amount' unless defined $amount;
   $per_employee{$name} = $amount;
   }
 ;;
 dd \%per_employee;
"
'Summary</h1><table border="1"><tr><th>Employee</th><th>999</th>' fail
+ed to parse at -e line 1.
{
  "Billy-Bob Toe" => "no amount",
  "Fred D. Poe" => "-5.03",
  "John Doe" => "-0.82",
  O => "1.23",
  Prince => 123,
}
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(Note that the  $rx_name regex for an actual, human name is very naive. (Update: See off-site Falsehoods Programmers Believe About Names.))

Update: Significant changes to example code:  $rx_th_open $rx_th_close regexes made more elegant (?); added rudimentary error handling; added corner and error test cases.