Your trying to open a non defined filehandle, if you want to retore the output, you have to save it before closing it.
Try printing fileno(STDOUT).

#!/usr/bin/perl -lw
use POSIX;
my $TRAP = POSIX::tmpnam();
print STDERR "STDOUT= ".fileno(STDOUT);
close(STDOUT);
print STDERR "STDOUT= ".fileno(STDOUT);
open(STDOUT, ">$TRAP")  || die("$!: $TRAP"); #+> didn't work
eval "print 'Waka waka!'";
seek(STDOUT, 0, 0);
print STDERR "STDOUT= ".fileno(STDOUT);
close(STDOUT);
open(STDOUT, ">-");
print STDERR "STDOUT= ".fileno(STDOUT);
open(INPUT, "<$TRAP") || die("$!: $TRAP");
$chldoutput = <INPUT>;
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Theres no errors or warnings, perhaps you want to save STDOUT before closing it

open(MYSTDOUT, ">&STDOUT");
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and later restore it with

open(STDOUT, ">&MYSTDOUT");
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$anarion=\$anarion;

s==q^QBY_^=,$_^=$[x7,print