One solution comes to mind.

Write a script that launches the critical script, and does something when it is no longer running.

#!/usr/bin/perl -w
use strict;

print "script started!\n";

my $result = system "critical.pl";

# if it comes here, then the script has died.

print "critical.pl is no longer running. (Exit code $result)\n";

#perhaps add code to send a mail to your address
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