If you really want do this (why?:), you can, and without resorting to subs or do blocks--but I wouldn't advise it. T'is fun though:)

#! perl -slw
use strict;

my @result;

sub dofirstcritical  { 
    print 'do first  critical returning ', $result[ 0 ]; 
    $result[ 0 ] 
}
sub dobackupcritical { 
    print 'do backup critical returning ', $result[ 1 ]; 
    $result[ 1 ] 
}
sub dobackupremainder{ print 'backup remainder done' }
sub dofirstremainder { print 'first  remainder done' }

for my $result ( [ 0, 0 ], [ 0, 1 ], [ 1, 0 ], [ 1, 1] ) {
    @result = @$result;
    
    eval{
        dofirstcritical() and ( dofirstremainder(), die 'Exiting 0' )
        or (        
            ( dobackupcritical() or die "main and backup failed" )
            and 
            ( dobackupremainder(), die 'Exiting 0' )
        )
    };
    print $@, $/;
}

__END__
P:\test>temp
do first  critical returning 0
do backup critical returning 0
main and backup failed at P:\test\temp.pl line 15.


do first  critical returning 0
do backup critical returning 1
backup remainder done
Exiting 0 at P:\test\temp.pl line 15.


do first  critical returning 1
first  remainder done
Exiting 0 at P:\test\temp.pl line 15.


do first  critical returning 1
first  remainder done
Exiting 0 at P:\test\temp.pl line 15.
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Note: The eval block is only there to captiure and record the dies and simulated exits.