open( LINKS, "+<", "filename" );
while (<LINKS>) {
   my $lastread = tell LINKS;  # keep track of where you are
   seek LINKS, 0, 2;  # jump to end-of-file
   ...
   # do stuff with current value of $_, including:
   print LINKS "another line of data\n";
   ...
   # when all done adding updates at the end...
   seek LINKS, $lastread, 0; # jump back for next read:
}