It does work because I have not chomped the line.

However the second open is in the wrong place:

### WRONG ###
while (<BIG>) {
  open OUT, ">outfile_" .$i++;
  if ( m/^\$\n$/ ) {

### CORRECT ###
open OUT, ">outfile_" .$i++;
while (<BIG>) {
  if ( m/^\$\n$/ ) {
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