Unless you are training yourself, it should be easier to use Parallel::ForkManager and its run_on_finish callback.

Manual way to do this is sequentially running waitpid with WHOHANG flag and checking its return value for all pids running. Example (untested):

foreach my $process (@child_pids) {
 if (waitpid($process->{PID}, WNOHANG)) {
  print "Process $process->{PROCESS} terminated\n";
 }
}
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