Incidentally, the script terminates after the third child exits without waiting for the sleep to complete.

If you have a signal handler set up, sleep (and many other system calls) will get interrupted by signals (returning error EINTR). This is a good thing, as it allows your signal handler to be called.

sub uninterruptible_sleep {
   my ($dur) = @_;
   my $until = time() + $dur;
   while (1) {
      $dur = $until - time();
      last if $dur <= 0;
      sleep($dur);
   }

   return 1;
}
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