The easiest solution would be the check if your string is defined prior to upload, a la:

while(<LINES>){                                  
    if (m/^--/){   
           push (my @data, [$id,$line]);
           if (defined $line) {                 
                $self->_loaddb(table => 'TABLE',
                               data=>\@data);
           }                                    

           $line= undef;                              
           $id++;                                  
    }                                            
    else{                                        
        chomp(my $string = $_);                    
        $line.=$string;                            
    }                                            
}
[download]

Update: Or, if you want to "Drop empty records, without incrementing the id", you could

while(<LINES>){                                  
    if (m/^--/){   
           next unless defined $line;
           push (my @data, [$id,$line]);
           $self->_loaddb(table => 'TABLE',
                          data=>\@data);

           $line= undef;                              
           $id++;                                  
    }                                            
    else{                                        
        chomp(my $string = $_);                    
        $line.=$string;                            
    }                                            
}
[download]