local $SIG{__DIE__} = sub {

  # get error message
  my $err = $_[0];

  # open error log or exit - you can't die here :)
  open(ERRLOG,'>>/path/to/errlog') || exit(0);

  # you may want to add information from the caller()
  # function here and add other info to log

  print ERRLOG "Error: $err\nplus whatever else you need...\n\n";
  close(ERRLOG);
  exit(0);
}