I think you could do it, but the query will not be very pretty. You could put the condition you have for the intermediate table into an exists clause of the table_c. Something like this

select a.value as a,b.value as b1,c11.value as c11
from table_a a
left join table_c as c11 on c11.value = 'a_1'
                                   and exists(select 1 from table_b b where c11.b_pk = b.pk and b.a_pk = a.pk)

I might be wrong but I think this is a valid translation.