The OP wants a C fgets() workalike. The main reason for this function in C is to avoid buffer overflows. Perl should dynamically expand the buffer as needed so technically this would seem to be unnecessary, although the OP's concern about DoS seems reasonable. It might be simpler to use an inside-out-object implementation something like this:

{
  my %buffers, %handles;
  sub fgets {
    my $fh = shift;
    my $max = shift;
    my $needed = $max - length $buffers{$fh};
    $buffers{$fh} .= do {local $/ = \$needed; <$fh>}
      if $needed > 0;
    open $handles{$fh}, '<', \$buffers{$fh}
      unless $handles{$fh};
    my $result = substr(readline $handles{$fh}, 0, $max);
    substr($buffers{$fh}, 0, length $result) = '';
    seek $handles{$fh}, 0, 0;
    return $result;
  }
}

# test code
open my $fh, '<', $0;
while(my $line = fgets $fh, 20) {
  print "[$line]";
}
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... but with error handling, of course. Need I mention that you shouldn't mix this fgets() with any other filehandle operations?