How can the concatenatation of a text and a NULL value return a non-null result? Assert 1
The concatenation operator || can concatenate any string type values, returning text. In Postgres, every type has a text representation and can be cast to text. Consequently, quoting the manual:

However, the string concatenation operator (||) still accepts non-string input, so long as at least one input is of a string type

Related:

How to concatenate columns in a Postgres SELECT?

Assert 2
Concatenating one or more NULL values makes the result NULL.
test=# SELECT (text 'foo' || NULL) IS NULL
test-#      , (text 'bar' || char '1' || NULL ) IS NULL
test-#      , (NULL::bigint || text 'baz') IS NULL;
 ?column? | ?column? | ?column? 
----------+----------+----------
 t        | t        | t

Question
Is it possible to concatenate a text and a NULL value and get a non-null result?
In other words, how is this possible?
test=# SELECT col IS NULL AS col_is_null
test-#     , (text 'foo' || col) IS NULL AS result_is_null
test-# FROM   tbl;
 col_is_null | result_is_null 
-------------+----------------
 t           | f

Applies to any Postgres version.
A client of mine stumbled over this, relying on the result to be NULL, and I found it intriguing enough to share.
It's a bit of a trick question as I know the answer.
Note: CASE or COALESCE catching NULL values are typically good style, but that's not what this question is about. It's about concatenation with an actual NULL value, with the concatenation operator || and still getting a non-null result.
That's because the system of CASTing array types in PostgreSQL is a bit weird (on a first sight) :-)

text || text[] makes both sides coerced to arrays.

CREATE TABLE tbl (col text ARRAY);

INSERT INTO tbl SELECT NULL;

SELECT col IS NULL AS col_is_null,
  (text 'foo' || col) IS NULL AS result_is_null
  FROM tbl;

 col_is_null | result_is_null 
-------------+----------------
 t           | f
(1 row)


Another example which may shed more light:

create temp table x as select 'foo' test, null::text[] col; 
SELECT test, col, test || col from x;
 test | col  | ?column? 
------+------+----------
 foo  | NULL | {foo}
(1 row)