#!/usr/bin/perl
use strict;
use warnings;
 
my $file = "regular.txt.out";
open my $fh, "<", $file or die "Unable to open $file: $!";
my($u_value, $p_value, $mc_value) = (undef) x 3;
 
while (my $line=<$fh>) {
    chomp $line;
    if ($line=~/\n\n\n/){
        ($u_value, $p_value, $mc_value) = (undef) x 3;
 
        print "\n";
    } elsif ($line=~/\bProcessing\s/) {
       $line=~s/\bProcessing\s\d+\.tx\.\d+: //;
       $u_value = $line;
        print "\n$u_value\n";
        undef $p_value;
    } elsif ($line=~/\bPhrase/) {
        $line=~s/\bPhrase: //;
        $line=~s/\"//g;
        if ($p_value) {
        print "\n" . ' ' x length $u_value;}
        $p_value=$line;
        print "\t$p_value";
        undef $mc_value;
     } elsif ($line=~/\s\s/ ) {
        if ($mc_value) {
        print "\n\t" . ' ' x length $p_value;}
        $mc_value=$line;
        print "\t$mc_value";
       } else {
     }
}
close $fh;
[download]

Somewhere along the way, your record separator changed from "EOU" to "\n\n\n". The first, presumably being unique in the data, was simple to test for. The latter is more difficult since you are processing the file one line at a time. I suppose you could keep a counter to see if three lines in a row contain nothing but a newline; but, it would be easier to change the record-separator variable ($/) to '\n\n\n'. I've done that below.

Also, '(\s\s)' is a glaring string to have in your data! You do know that all those characters have special meaning in a regular expression: /(\s\s)/ matches and keeps two whitespace characters. So to match them literally, you need to escape them. I've done that below too. (In my previous reply, I did think to myself that /\s\s/ was not a very definitive expression, but I kept it because you had it.)

I think the following does what you want. Note two assumptions: 1) That you always want to print the $u_val, even if there isn't a following $p_val/$m_val pair. 2) That $m_val always follows $p_val.

use strict;
use warnings;

my $file = "z.txt";
open my $fh, "<", $file or die "Unable to open $file: $!";
my ($p_val, $m_val);
{ local $/ = '\n\n\n';
  while (<$fh>) {                   # read until three newlines
     foreach (split/\n/) {          # split it into individual lines
        if (s/\bProcessing\s\d+\.tx\.\d+: //) {
            print "$_\n";           # print the u_value immediately
        } elsif (s/\bPhrase: //) {
            s/"//g;                 # note: no need to escape "
            $p_val = $_;            # keep it
        } elsif (/\(\\s\\s\)/) {
            $m_val = $_;            # keep it
            if (defined $p_val) {
               print "\t$p_val\t$m_val\n";  # print if we have both
            }
            ($p_val, $m_val) = (undef)x2;
        }
     }
  }
}
close $fh;
__END__
Pulmonary embolism at the time of hip replacement
        Pulmonary embolism      (\s\s)1000 D0076131:PULMONARY EMBOLISM
+ Disease or Syndrome
        of hip replacement      (\s\s)1000 D0554893:HIP REPLACEMENT (S
+TATUS POST HIP REPLACEMENT) Finding
[download]

Thank you hbm. Yes, my record has changed. I started with a tab delimited file with "EOF." record separator but it didn't work out since the script processed only up to 14,000 lines and then exit without any error. Plus, I was missing one of the components in my original text. So, I started working on another output format from the same text. In the new format, records are separated with two blank lines so I thought to use \n\n\n as the separator
For some reason when I tried to post my question spaces were being eliminated in my post so by typing (\s\s) I was trying to imply that in my real record there are two spaces before my mapping starts.Sorry, my bad!
Thank you again for all your help and explanation. Is there any book you recommend for a Perl beginner like me to start with? I started with Perl Programming for Medicine and Biology" but I think some basic (and fundamental) concepts are not covered in that book.