$sth->prepare("INSERT INTO Blah (a,b,c) VALUES (?,?,?)");
tie *TSV, 'File::ReadBackwards', $filename;
while (<TSV>) {
  my @insert = processRow($_); #this splits the records into an array and does some data cleaning
  $sth->execute(@insert);
  #And check for errors and all that...
  truncate $filename, tell TSV; #pops the last line
}

untie *TSV;
unless ($errors) { unlink $filename; }