--> 测试数据：[tb]
IF OBJECT_ID('[tb]') IS NOT NULL DROP TABLE [tb]
GO 
CREATE TABLE [tb]([序号] INT,[低保编号] VARCHAR(16),[姓名] VARCHAR(6))
INSERT [tb]
SELECT 1,'3711000102080001','曹现菊' UNION ALL
SELECT 2,NULL,'宋祥华' UNION ALL
SELECT 3,NULL,'宋志昊' UNION ALL
SELECT 1,'3711000102080002','陈斌' UNION ALL
SELECT 2,NULL,'高丽' UNION ALL
SELECT 3,NULL,'陈宇' UNION ALL
SELECT 1,'3711000102080003','刘田信' UNION ALL
SELECT 2,NULL,'郁桂英' UNION ALL
SELECT 3,NULL,'刘婷婷' UNION ALL
SELECT 4,NULL,'刘源' UNION ALL
SELECT 1,'3711000102080004','鲁彬' UNION ALL
SELECT 2,NULL,'徐翠霞'
--------------开始查询--------------------------
;WITH cte AS
(
SELECT *,row=ROW_NUMBER() OVER(ORDER BY GETDATE()) FROM [tb]
)
SELECT [序号],
低保编号=ISNULL(低保编号,(SELECT TOP 1 低保编号 FROM cte WHERE 低保编号 IS NOT NULL AND row<t.row ORDER BY row DESC)),
姓名 
FROM  cte t

----------------结果----------------------------
/* 
序号          低保编号             姓名
----------- ---------------- ------
1           3711000102080001 曹现菊
2           3711000102080001 宋祥华
3           3711000102080001 宋志昊
1           3711000102080002 陈斌
2           3711000102080002 高丽
3           3711000102080002 陈宇
1           3711000102080003 刘田信
2           3711000102080003 郁桂英
3           3711000102080003 刘婷婷
4           3711000102080003 刘源
1           3711000102080004 鲁彬
2           3711000102080004 徐翠霞

(12 行受影响)

*/

------解决方案--------------------
非游标不行吗？

------解决方案--------------------
SQL code

--> 测试数据：[test]
if object_id('[test]') is not null 
drop table [test]
create table [test](
[序号] int,
[低保编号] varchar(16),
[姓名] varchar(6)
)
insert [test]
select 1,'3711000102080001','曹现菊' union all
select 2,null,'宋祥华' union all
select 3,null,'宋志昊' union all
select 1,'3711000102080002','陈斌' union all
select 2,null,'高丽' union all
select 3,null,'陈宇' union all
select 1,'3711000102080003','刘田信' union all
select 2,null,'郁桂英' union all
select 3,null,'刘婷婷' union all
select 4,null,'刘源' union all
select 1,'3711000102080004','鲁彬' union all
select 2,null,'徐翠霞'


alter table test add id int identity
go
with t
as(
select 
    ROW_NUMBER()over(order by getdate())-[序号] as px,
    * 
from
    test
), 
m as
(
select 
    px,
    [序号],
    ISNULL([低保编号],(select [低保编号] from t b 
    where [序号]=1 and a.px=b.px )) [低保编号],
    [姓名]
from 
    t a
)
update test 
set test.[低保编号]=a.[低保编号] from m a where test.id=a.px+a.序号

go
alter table test drop column id
go
select * from test
/*
序号    低保编号    姓名
-----------------------------------
1    3711000102080001    曹现菊
2    3711000102080001    宋祥华
3    37110001