First of all, it helps to characterize the problem: you're building a very simple state machine. Each called subroutine is a new state, and the return value from each called function is the input which selects the next transition. In this case, you want FALSE to trigger a transition to the next state, and TRUE to trigger a transition to the accept state:

    (s0)- F ->(s1)- F ->(s2)-[...]
      |         |         |
      +---------+---------+--[...]- T ->(accept)
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In this case, you can implement that with a list of function pointers and a loop:

    sub outer {
        my @funcs = (\&f1, \&f2, \&f3, ...);
        my $result = 0;
        
        for $f (@funcs) {
            $result = $f->();
        last if $result;
        }
        
        return ($result);
    }
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And more generally, you can use a hash as a transition table:

    sub outer {
        %trans = _get_transition_table();
        
        my $f = $trans{'start'};
        my $result = 0;
        
        do {
            $result = $f1->();
            my $state = ($result) ? "$f.true" : "$f.false";
            $f = $trans{ $state };
        } while ($f);
        
        return ($result);
    }
    
    sub _get_transition_table {
        my $f1 = \&f1;
        my $f2 = \&f2;
        my $f3 = \&f3;
        [...]
        
        return (
            "start"     =>  $f1,
            "$f1.true"  =>  0,
            "$f1.false" =>  $f2,
            [...]
        );
    }
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which allows for multiple output values per function, and state diagrams that are more complicated than just a simple list.

If you want to pass parameters to the functions, pass a listref and have the called functions and use it as an argument list, a stack, a queue, or whatever:

    sub caller {
        [yadda yadda]
        
        my $args = [];
        
        do {
            $result = $f->($args);
            [yadda yadda]
        } while ($f);
        
        return ($result);
    }
    
    sub as_list {
        my $args = shift;
        
        my ($arg1, $arg2, $arg3) = @$args;
        @$args = ();
        
        [...]
    }
    
    sub as_stack {
        my $args = shift;
        my $item = pop @$args;
        
        [...]
        
        push @args, $result;
        
        return ([true|false]);
    }
    
    sub as_queue {
        my $args = shift;
        my $item = shift @$args;
        
        [...]
        
        push @args, $result;
        
        return ([true|false]);
    }
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