I managed to write some code that doesn't use a cursor, so hooray for performance 🙂

SELECT

ID= tmp.ID

,Value= t3.[Value]

FROM

(SELECT t1.[ID]

,MaxID = MAX(t2.ID)

FROM[dbo].[Test] t1

INNER JOIN[dbo].[Test] t2 ON [t1].[ID] >= [t2].[ID] AND t2.[Value] IS NOT NULL

GROUP BY t1.[ID]) tmp

INNER JOIN [dbo].[Test] t3 ON tmp.[MaxID] = t3.[ID]

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