This works for me in my linux shell:

$ cat prog.pl
use strict;
use warnings;

my $cnt = 1;
while (<>) {
    s/$/sprintf '%04d', $cnt++/e if /^\*+$/;
    print;
}
$
$
$ cat file.txt
foo boo
***
goo hoo
***********************************

bloo
$
$
$ perl prog.pl file.txt
foo boo
***0001
goo hoo
***********************************0002

bloo
$
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