Perhaps if you use it twice with a little tweak. 😉

SELECT

S.ID

,LTRIM(ISNULL(Y.Item, X.Item)) AS OUT_STRING

FROM @SAMPLE S

CROSS APPLY dbo.DelimitedSplit8K(S.STRING,CHAR(39)) AS X

OUTER APPLY (SELECT s.Item

FROM (SELECT LTRIM(X.Item) Item) i

CROSS APPLY dbo.DelimitedSplit8K( i.Item, ' ') s

WHERE X.Item LIKE '% '

AND LEN(s.Item) > 0) Y

WHERE LEN(X.Item) > 0;