As others have mentioned, you probably misunderstand the difference between opening a file and reading it into memory. If you simply want to read to the 10000th '>', this might work.

my $big_line = ""
# Set the newline character to '>'
$/ = '>';

open fh, $filename;
for (my $i = 0; i < 10000; i++) {
  $big_line .= <fh>;
}

$/ = "\n";
close fh;
[download]

Now $bigline will contain everything up to the 10000th '>'. I'm not sure that this will work if you've been having file troubles, but it's probably worth a try.