SQL Server 2019

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    CREATE TABLE dbo.MyBigTable
    (
      MyKey bigint NOT NULL,
      x char(1),
      -- OtherColumns here,
      CONSTRAINT PK_MyBigTable PRIMARY KEY (MyKey)
    ); -- Partition stuff here
    
    INSERT dbo.MyBigTable(MyKey) 
      SELECT TOP (95008) ROW_NUMBER() OVER (ORDER BY s1.object_id)
      FROM sys.all_objects AS s1
      CROSS JOIN (SELECT TOP (1000) * FROM sys.all_objects) AS s2;
      
      DELETE dbo.MyBigTable WHERE MyKey IN (10, 50005)
95010 rows affected

DECLARE @BatchSize int = 10000;

;WITH x AS
(
  SELECT rn = ROW_NUMBER() OVER (ORDER BY MyKey),
         s  = FIRST_VALUE(MyKey) OVER (ORDER BY MyKey),
         ln = ROW_NUMBER() OVER (ORDER BY MyKey DESC),
         MyKey
    FROM dbo.MyBigTable
)
SELECT BatchNumber = ROW_NUMBER() OVER (ORDER BY rn),
       RangeStart  = COALESCE(LAG(MyKey,1) OVER (ORDER BY MyKey)+1,s),
       RangeEnd    = MyKey,
       Processed   = 0
INTO dbo.UpdatingQueue
FROM x WHERE rn % @BatchSize = 0 OR ln = 1
ORDER BY BatchNumber;

CREATE UNIQUE CLUSTERED INDEX CIX_UpdatingQueue 
  ON dbo.UpdatingQueue(RangeStart, RangeEnd);
10 rows affected

-- now your batch can say:

DECLARE @BatchNumber int;
SELECT @BatchNumber = MIN(BatchNumber)
  FROM dbo.UpdatingQueue 
  WHERE Processed = 0;

WHILE @BatchNumber IS NOT NULL
BEGIN
  -- need try/catch here obviously
  UPDATE mbt SET x = 'x'
    FROM dbo.MyBigTable AS mbt
    INNER JOIN dbo.UpdatingQueue AS q
    ON mbt.MyKey >= q.RangeStart
    AND mbt.MyKey <= q.RangeEnd
    WHERE q.BatchNumber = @BatchNumber
      AND q.Processed = 0;
    
  UPDATE dbo.UpdatingQueue
    SET Processed = 1 
    WHERE BatchNumber = @BatchNumber;
    
  SET @BatchNumber += 1;
  
  SELECT @BatchNumber = MIN(BatchNumber)
    FROM dbo.UpdatingQueue
    WHERE Processed = 0;
  -- add a delay, explicit checkpoint / backup log here, what have you
END
-- and the batch can be interrupted, because if
-- you stop it and start it again tomorrow or
-- next week, it will pick up where it left off.
95016 rows affected

-- spot check
SELECT * FROM dbo.MyBigTable WHERE MyKey % 1000 = 0;



MyKey
x


1000
x

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MyKey	x
1000	x
2000	x
3000	x
4000	x
5000	x
6000	x
7000	x
8000	x
9000	x
10000	x
11000	x
12000	x
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20000	x
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25000	x
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27000	x
28000	x
29000	x
30000	x
31000	x
32000	x
33000	x
34000	x
35000	x
36000	x
37000	x
38000	x
39000	x
40000	x
41000	x
42000	x
43000	x
44000	x
45000	x
46000	x
47000	x
48000	x
49000	x
50000	x
51000	x
52000	x
53000	x
54000	x
55000	x
56000	x
57000	x
58000	x
59000	x
60000	x
61000	x
62000	x
63000	x
64000	x
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70000	x
71000	x
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73000	x
74000	x
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77000	x
78000	x
79000	x
80000	x
81000	x
82000	x
83000	x
84000	x
85000	x
86000	x
87000	x
88000	x
89000	x
90000	x
91000	x
92000	x
93000	x
94000	x
95000	x