It would be more reliable to set the exit code appropriately.

# special.pl

my $success = 1;

...
if (...) {
   $success = 0;
}
...

exit $success ? 0 : 1;
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Then all you need is

perl special.pl && perl backup.pl
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Note that if special.pl dies for any reason, the exit code will be set to something nonzero, so even unexpected failures will also prevent backup.pl from executing.