my @cmd = ("/bin/ls", "/doesntexist");

use vars qw(*OLDERR);
open OLDERR, ">&STDERR";
open STDERR, ">/dev/null";

  # STDERR suppressed
system(@cmd);

*STDERR = *OLDERR;

print STDERR "stderr is open\n";

  # STDERR should be open - but isn't
system(@cmd);

##</code><code>##

stderr is open