Here's a low tech solution:

#!/usr/bin/perl -w
use strict;
pipe READER,WRITER or die;
my @output;
if (my $pid = fork) {
   # parent, close the WRITER and read from READER
   close WRITER;
   while(<READER>) {
      chomp;
      push(@output,$_);
      print "adding $_ to \@output\n";
   }
   # parent now has the system() output in @output,
   # as well as the line from the child's print()
} else {
   # child, dup WRITER to STDOUT and close WRITER, then
   # exec() your system call
   open(STDOUT,">&WRITER");
   close WRITER;
   print STDOUT "This is the child running ls\n";
   exec("/bin/ls");
}
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Update: I guess I should point out that the child could be mixing perl STDOUT writes with the system calls' STDOUT writes. I think the original poster wanted to run a code ref, including system calls and have all the writes to STDOUT output to a perl variable.