You didn't show us the parser code that produces $line[0]. The best place for this would be in the parser.

However, here is a quick fix to preprocess the text file while reading it. (I am assuming you read it line by line):

while (my $line = <$fh>) {
  if ($line =~ tr/"//) {
    # This block will be executed if there is exactly one double-quote
+ in the line
    while (1) {
      my $nextline = <$fh>;
      die unless defined $nextline;
      $nextline =~ s/^\s+/ /; # remove indent
      $line .= $nextline; # join lines
      break if ($nextline =~ tr/"//) % 2 == 1;
    }
  }

  # now parse the $line just like you would normally do using the code
+ that you did not show us ;-)
  parse_line();
}
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