You are using the right functions, but the wrong JOIN. If you (possibly) don't have rows on one side of the JOIN & you want to keep the rows from the other side of the JOIN & use NULLs to "pad" rows, you'll need an OUTER JOIN:

with outside as (
    select json_array_elements('[[],[11],[21,22,23]]') aa,
           json_array_elements('[1,2,3]') bb
) 
select    a, bb
from      outside
left join json_array_elements_text(aa) a on true

Note: it may seem strange to see on true as the joining condition, but it is actually quite general, when you are using LATERAL joins (which is implicit when you use a set returning function (SRF) directly in the FROM clause).

http://rextester.com/KNW13145

Edit: your original query does not involve a JOIN directly, but worse: you use a SRF in the SELECT clause. This is almost like a CROSS JOIN, but actually it has its own rules. Don't use that unless you know exactly what you are doing and why you need that.

This is not a bug. json_array_elements_text('[null]') returns null, json_array_elements_text('[]') does not return anything.

with outside as (
    select (
        json_array_elements('[[],[11],[21,22,23]]'::json)) aa, 
        json_array_elements('[1,2,3]'::json) bb
) 
select elem as aa, bb
from outside,
json_array_elements_text(case when aa::text = '[]' then '[null]'::json else aa end) elem;

 aa | bb 
----+----
    | 1
 11 | 2
 21 | 3
 22 | 3
 23 | 3
(5 rows)    

Working through my own problem, i've got one possible answer, but it seems like a mess

With initial as (select '[[],[11],[21,22,23]]'::json as a, '[1,2,3]'::json as b),
    Q1 as (select json_array_elements(a) as aa, json_array_elements(b) bb from initial),
    Q2 as (select ARRAY[aa->>0, aa->>1, aa->>2] as aaa, bb as bbb, ARRAY[0,1,2] as ccc from q1), 
    -- where the indicices are computed in a separate query by looping from 0 to json_array_length(...)
    Q3 as (select unnest(aaa) as aaaa, bbb as bbbb, unnest(ccc) as cccc from q2)

Select aaaa, bbbb from q3 where aaaa is not null or cccc = 0