Without forking, it would be

open(my $fh_x, '<', 'x') or die $!;
while (<$fh_x>) {
    chomp( my $linex = $_ );
    open my $fh_y,   '<', 'y'    or die $!;
    open my $fh_out, '>', $linex or die $!;
    while (<$fh_y>) {
       chomp( my $liney = $_ );
       print $fh_out ("$linex$liney\n");
    }
}
[download]

So with forking, it would be

open(my $fh_x, '<', 'x') or die $!;
while (<$fh_x>) {
    $pm->start and next;
    chomp( my $linex = $_ );
    open my $fh_y,   '<', 'y'    or die $!;
    open my $fh_out, '>', $linex or die $!;
    while (<$fh_y>) {
       chomp( my $liney = $_ );
       print $fh_out ("$linex$liney\n");
    }
    $pm->finish   
}
[download]

Since every thread reads file y, you could preload it into memory to save the threads from all doing the same work.

Without forking, it would be

my @y;
{
   open my $fh_y, '<', 'y' or die $!;
   chomp( @y = <$fh_y> );
}


open(my $fh_x, '<', 'x') or die $!;
while (<$fh_x>) {
    chomp( my $linex = $_ );
    open my $fh_out, '>', $linex or die $!;
    for my $liney (@y) {
       print $fh_out ("$linex$liney\n");
    }
}
[download]

So with forking, it would be

my @y;
{
   open my $fh_y, '<', 'y' or die $!;
   chomp( @y = <$fh_y> );
}


open(my $fh_x, '<', 'x') or die $!;
while (<$fh_x>) {
    $pm->start and next;
    chomp( my $linex = $_ );
    open my $fh_out, '>', $linex or die $!;
    for my $liney (@y) {
       print $fh_out ("$linex$liney\n");
    }
    $pm->finish   
}
[download]

Update: Added preloading version.
Update: Fixed bug mentioned in reply.

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