Consider this refactored version of your Perl script. (It hasn't been tested at all.)

use strict;
use warnings;
use autodie qw( open close );
use open qw( :encoding(UTF-8) :std );

my %terms_in; # Hash of hash of terms in each file

my $terms_file = 'array.txt';

open my $fh1, '<', $terms_file;

while (my $record = <$fh1>) {
    my ($file, $term) = $record =~ m/^(\S+)\s+(\S+)/;

    $terms_in{ $file }{ $term } = 1;
}

close $fh1;

FILE:
for my $file (keys %terms_in) {
    open my $fh2, '<', $file;

    while (my $line = <$fh2>) {
        for my $term (keys %$terms_in{ $file }) {
            if (index $line, $term) {
                print "Term $term found in file $file\n";

                # Don't search terms that have already been found...
                delete $terms_in{ $file }{ $term };
            }
        }

        # Don't keep searching file once all terms have been found...
        if (scalar keys %$terms_in{ $file } == 0) {
            close $fh2;

            next FILE;
        }
    }

    close $fh2;
}

# At this point, what remains in %terms_in are all the terms that
# were not found in their respective files, which might be useful.

exit 0;
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