$/ doesn't help. (And don't forget the RHS needs to be a reference: local $/ = \80;)

local $/ = \10;  # Easier to visualize than 80.
print "$_\n" while <DATA>;
__DATA__
abcdefghijklm
ABCDEFGHIJKLM
[download]

outputs

abcdefghij
klm
ABCDEF
GHIJKLM
[download]

instead of

abcdefghij
klm
ABCDEFGHIJ
KLM
[download]

read (or unbuffered sysread) can do it with some coaxing.

my $wrap_len = 10;

my $buf = '';
LOOP:
for (;;) {
   while (length($buf) < $wrap_len+1) {
      my $rv = read(DATA, $buf, $wrap_len+1-length($buf), length($buf)
+);
      die if not defined $rv;
      last LOOP if not $rv;
   }
   
   ($buf =~ s/^(.*)\n// || $buf =~ s/^(.{0,$wrap_len})//)
      and print("$1\n");
}

print($buf);

__DATA__
abcdefghijklm
ABCDEFGHIJKLM
[download]

The +1 avoids adding a \n before another \n.