The line my$a=$_; does nothing useful, since $_ is uninitialised. As Anonymous Monk says, you need to read from STDIN. For example:

#! perl
use strict;
use warnings;

print "Enter the target word: ";
chomp(my $target = <STDIN>);

my $in_file = 'words.txt';
open(my $in, '<', $in_file) or die "Cannot open file '$in_file' for re
+ading: $!";
my @matches;

while (<$in>)
{
    chomp;
    push @matches, $_ if $target =~ /$_/i;
}

close $in                   or die "Cannot close file '$in_file': $!";

@matches = sort { length $a <=> length $b } @matches;
print "The closest match is:  ", $matches[-1], "\n";
[download]

If the file “words.txt” contains:

fal
falle
fall
[download]

then, when “fallen” is entered from the keyboard, the output of the above script is:

 2:31 >perl 454_SoPW.pl
Enter the target word: fallen
The closest match is:  falle

 2:31 >
[download]

Hope that helps,

Update: Fixed error in sort: changed > to <=>. Also changed the order of words in the input file.