my $filenumber = 0;
my $filename = 'FILE';
my $newfile = $filename.$filenumber;
my $nextnumber = $filenumber++;
[...]

while (true) { # daemon-Schleife
      while (-e $newfile) { # Existiert FILE0, dann FILE1.
	  $nextnumber;
	  $newfile.$filenumber;
      }