Rather than a workaround, you may want to read perlopentut (gentle) and open.

Update with code: As the docs for open point out, this is NOT the preferred way to do it, but does this perhaps do what you wanted (preserve the prior content of main_log.txt, and append the content of sub_log.txt)?

# 795500

# $| = 1;        # autoflush

my $main_log = 'main_log.txt';
my $sub_log = 'sub_log.txt';

open LOGFILE, '<', $main_log
     or die "Cannot open $main_log for read, $!";

my $prior_content;
while (<LOGFILE>) {
    $prior_content = $prior_content . $_;
}
close( LOGFILE );

open LOGFILE, '>', $main_log
     or die "Cannot open $main_log for write, $!";

print LOGFILE $prior_content;
print LOGFILE "\n---\n";

print LOGFILE "\n\tStart: Coming from the script.\n";

open( SUBLOG, '<', $sub_log )
  or die( "Error: Cannot open sub_log" );

print LOGFILE $_ while( <SUBLOG> );

close( SUBLOG );

print LOGFILE "\n\tEnd of sub_log as read by script.\n";

print LOGFILE "\tEnd: Coming from the script.\n";
close( LOGFILE );
[download]

If it's not what you intended, you may wish to deal with the problems almut pointed out... AND clarify your question (because your code doesn't do so for me).