If you formatted your code correctly, the reason becomes obvious.

You've added your until clause to the end of your foreach loop:

#!/usr/bin/perl-w 
## To chop a sentence at intervals of 4-letter and to print results:
use strict;
my $sentence="BEAR CALF DEER FEAR GEAR HEAR";
## To remove blank spaces:  # Line 5  
$sentence=~ s/\s//igs;
print"\n Words are:  \n";
do {
    my @four=$sentence=~ /[a-zA-Z]{4}/igs; # Line 9 
    foreach my $word(@four) {
        print"\n $word: ";
        my $length=length($word);
        print"\n Length of the word= $length\n\n";
        my $output="Words .txt";                  # Line 14
        unless (open(RESULT,">$output")){
            print"Cannot open file\"$output\".\n\n";   # Line 16
            exit;
        }
        print RESULT"\n Words are:  \n
        Word: $word; Length of the word= $length\n\n";
        close(RESULT);  # Line 21 
    } until ( my $word=~ /^.*$/); # Line 22  
    exit;
}
[download]