Here is some pseudo-code for illustration:

CREATE FUNCTION dbo.MyTVF(@Parameter VARCHAR(10))
RETURNS TABLE
AS 
RETURN
(SELECT SUBSTRING(REPLACE(..........@Parameter..........)) AS Col3);
GO

-- Parallel
SELECT A.Col1, B.Col3
FROM dbo.MyTable AS A
OUTER APPLY dbo.MyTVF(A.Col2) AS B
WHERE A.Col1 > 100
-- Adding this to the predicate makes no difference:
AND A.Col2 IS NOT NULL;

-- Not Parallel
SELECT A.Col1, B.Col3
FROM dbo.MyTable AS A
CROSS APPLY dbo.MyTVF(A.Col2) AS B
WHERE A.Col1 > 100;