The following might help. I don't understand why you are forking, so I have not done so, but you could add forking inside the loop if you want to, as long as you increment and reset $index_y in the main process so that it is coordinated across all the child processes.

#!/usr/bin/perl
use strict;
use warnings;

open(my $y, "<", "y") or die "y: $!";
my @y = <$y>;
close($y);

my $index_y = 0;

open(my $x, "<", "x") or die "x: $!";

foreach (<$x>) {
    chomp;
    open(my $output, ">", "$_") or die "$_: $!";
    print $output "$_$y[$index_y]";
    close($output);
    $index_y++;
    $index_y = 0 if($index_y > $#y);
}

close($x);
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