This will do it, but it will get rid of the returns in the data. If that's not your intention, you'll need to be a bit more fancy than the "." operator.

my $number_of_fields = 10;
my $hold = "";
while(<FILE>) {
  chomp;
  my $line = $hold.$_;
  my @line = split("\t", $line);
  if (@line < $number_of_fields) {
    $hold = $line;
    next;
  }
  $hold = "";
  do stuff
}
[download]

Update:
Forgot to mention that you need to know the # of fields that you are expected to have. And error checking would be desired.