Indeed, there's this:

sub _debug_fd {
    return fileno STDERR unless defined $cur_self;
    if ( _debugging && !defined $cur_self->{DEBUG_FD} ) {
        my $fd = select STDERR;
        $| = 1;
        select $fd;
        $cur_self->{DEBUG_FD} = POSIX::dup fileno STDERR;
        _debug("debugging fd is $cur_self->{DEBUG_FD}\n")
          if _debugging_details;
    }
    return fileno STDERR unless defined $cur_self->{DEBUG_FD};
    return $cur_self->{DEBUG_FD};
}
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It's called a number of places as follows or similar:

$op->open_pipe( $self->_debug_fd )
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It seems it's used to provide a means for post-fork but pre-exec code in the child to display debug messages without causing issues if the child's STDERR is redirected. For example, you wouldn't want some of the debug messages of run \@cmd, "2>", "err.txt" to end up on STDERR and some of them to end up in `err.txt`.