Works OK for me. I tried:

use warnings;
use strict;

BEGIN {
  open(STDERR, ">stderr2.log")
    or die "Failed to open log file";
}

print STDERR "Oops!\n";
system ('nosuchprogram');

close STDERR;
[download]

In stderr2.log was:

Oops!
'nosuchprogram' is not recognized as an internal or external command,
operable program or batch file.
[download]

Running on 5.10.0 Windows.

update: I guessed that "subscript" meant another script being called as a child process, but could be wrong.