I think I'm able to follow you:

$ ./1.term.pl 
Sleeping 1 seconds ...
Print finishing normally (sleep 1 completed)
[1]+  Done                    gedit 1.term.pl
$ ./1.term.pl 
Sleeping 1 seconds ...
Print finishing normally (sleep 1 completed)
$ ./1.term.pl 
Sleeping 3 seconds ...
^C
$ cat cleanup_handler_log.txt 
DESTROY() called. Cleaning up...
DESTROY() called. Cleaning up...
[download]

Destroy gets called when the sleep amount expires. I raised the sleep number to 3 and hit it with control-c and did not get the destroy called. Why is that? Finally, I ran it in the terminal and x'ed out of it while it was running and did see the destroy message:

$ cat cleanup_handler_log.txt 
DESTROY() called. Cleaning up...
DESTROY() called. Cleaning up...
DESTROY() called. Cleaning up...
$
[download]

Script I was running:

$ cat 1.term.pl 
#!/usr/bin/perl -w
use 5.011;
use FindBin;
use File::Spec;

my $log_fn = File::Spec->catfile($FindBin::Bin, "cleanup_handler_log.t
+xt");
open my $LOG, '>>', $log_fn or die "Failed to open log '$log_fn' for a
+ppending ($!)\n";
binmode $LOG;
$LOG->autoflush(1); # disable buffering

package Blah;{
    sub new {
        return bless {}, shift;
    }
    sub DESTROY {
        print $LOG "DESTROY() called. Cleaning up...\r\n";
    }
}

my $obj = Blah->new;

my $sleep_time = 3; 
print "Sleeping $sleep_time seconds ...\n";
sleep $sleep_time;
print "Print finishing normally (sleep $sleep_time completed)\n";
$
[download]