SQL Server 2019

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WITH your_table(ID,STOREDATE,VALUE,INFO)
AS
(
SELECT 1122,'1/1/2020',2,'DONE' UNION ALL
SELECT 1122,'1/2/2020',7,'DONE' UNION ALL
SELECT 1122,'1/3/2020',1,'DONE' UNION ALL
SELECT 1122,'1/4/2020',8,'DONE' UNION ALL
SELECT 4466,'1/1/2020',2,'DONE' UNION ALL
SELECT 4466,'1/2/2020',7,'DONE' UNION ALL
SELECT 4466,'1/3/2020',1,'DONE' UNION ALL
SELECT 4466,'1/4/2020',8,'DONE'
),

CTE AS
(
    SELECT ID,
    STOREDATE,
    VALUE,
    CASE 
        WHEN VALUE = 8 THEN 0
        WHEN VALUE + LAG(VALUE) OVER(ORDER BY ID, STOREDATE) = 8 
            AND ID = LAG(ID) OVER(ORDER BY ID, STOREDATE) THEN 0
        WHEN VALUE + LEAD(VALUE) OVER(ORDER BY ID, STOREDATE) = 8 
            AND ID = LEAD(ID) OVER(ORDER BY ID, STOREDATE) THEN 0
        ELSE VALUE
    END VALUE2,
    INFO
    FROM your_table
)

SELECT *,
CASE 
    WHEN 
        (
            SELECT COUNT(*) FROM CTE A 
            WHERE A.VALUE2 = 0 AND A.STOREDATE < B.STOREDATE
            AND A.ID = B.ID
        ) >= 1 AND B.VALUE = 8 THEN B.VALUE
    ELSE B.VALUE2
END VALUE3
FROM CTE B

ID	STOREDATE	VALUE	VALUE2	INFO	VALUE3
1122	1/1/2020	2	2	DONE	2
1122	1/2/2020	7	0	DONE	0
1122	1/3/2020	1	0	DONE	0
1122	1/4/2020	8	0	DONE	8
4466	1/1/2020	2	2	DONE	2
4466	1/2/2020	7	0	DONE	0
4466	1/3/2020	1	0	DONE	0
4466	1/4/2020	8	0	DONE	8