use strict;
use warnings;

my $cnt = 1;
while (<>) {
    s/$/sprintf '%04d', $cnt++/e if /^\*+$/;
    print;
}

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Update: The above code functionally satisfies the OP specification. Thanks to ikegami for demonstrating several optimization techniques below.

In reply to Re: Numbering instances of a String in a file by toolic
in thread Numbering instances of a String in a file by Anonymous Monk

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