Perhaps you could set $SIG{__DIE__}. Like this:

sub mysub {
   my $error = shift;
   print STDERR "mail stuff here..\n";
   print STDERR "Error message: $error";
   print STDERR "End of mail\n";
   die $error;
}

local $SIG{__DIE__} = \&mysub;
open(TMPFILE,"<datafile.txt") || die "Cant open: $!";
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