Using Craig's setup, is this what you are looking for?

declare @RunDate date;

set @RunDate = '2014-07-22'

select dateadd(week,datediff(week,0,dateadd(day,-1,@RunDate)),0)

IF OBJECT_ID ('tempdb..#SampleData') IS NOT NULL

DROP TABLE #SampleData

CREATE TABLE #SampleData (PERSON INT ,dt DATETIME,[PAYTYPE] VARCHAR(20) ,[ID] INT)

INSERT INTO #SampleData

SELECT 12913,'07/21/2014','Regular',101

UNION ALL SELECT 12913,'07/22/2014','Regular',102

UNION ALL SELECT 12913,'07/23/2014','Regular',103

UNION ALL SELECT 12913,'07/24/2014','Regular',104

UNION ALL SELECT 12913,'07/25/2014','Regular',105

UNION ALL SELECT 12913,'07/26/2014','Regular',104

UNION ALL SELECT 12913,'07/27/2014','Regular',105

UNION ALL SELECT 12913,'07/28/2014','Regular',101

UNION ALL SELECT 12913,'07/29/2014','Regular',102

UNION ALL SELECT 12913,'07/30/2014','Regular',103

UNION ALL SELECT 12913,'07/31/2014','Regular',104

UNION ALL SELECT 12913,'08/01/2014','Regular',105

SELECT

*

FROM

#SampleData

WHERE

dt >= dateadd(week,datediff(week,0,dateadd(day,-1,@RunDate)),0) and

dt <= @RunDate

ORDER BY

PERSON,

dt,

ID;

UPDATE #SampleData SET

PAYTYPE = 'Regular2'

OUTPUT

deleted.PERSON,

deleted.dt,

deleted.PAYTYPE,

deleted.ID

INTO

#SampleData

WHERE

PAYTYPE = 'Regular'

AND dt >= dateadd(week,datediff(week,0,dateadd(day,-1,@RunDate)),0) and

dt <= @RunDate;

SELECT

*

FROM

#SampleData

ORDER BY

PERSON,

dt,

ID;