while(<FILE>)
{
  if(/matches/)   # use of $_, everything is ok
  {
     $object->doSomething($part_of_line);
  }

  print "$_\n";   # here $_ has a value of undef and causes problems
}

##</code><code>##

sub doSomething
{
  ...
   open(FILE2, $file2);
   while(<FILE2>)
   {
      # do more stuff
   }
   # At this point in the code, $_ is undef and since $_ is
   # global...
}