And here you have a different version that will use only the rows needed. Ideally, you shouldn't have to create the PersonList set and you'll have a table with them that you can join to your personstatus table by something different than the name column.

I really hope that you have a different database design than the one showed in here.

DECLARE @FromDt date = '20130101',

@ToDt date = '20140101';

WITH cteDays AS(

SELECT *, DATEDIFF(DD,

CASE WHEN @FromDt < DateAdded THEN DateAdded ELSE @FromDt END,

CASE WHEN @ToDt > InactivationDate THEN InactivationDate ELSE @ToDt END) + 1 numdays

FROM personstatus

WHERE InactivationDate >= @FromDt

AND DateAdded <= @ToDt

),

PersonList AS(

SELECT DISTINCT name

FROM personstatus

)

SELECT p.name, SUM( CASE WHEN numdays > 0 THEN numdays ELSE 0 END) numdays

FROM PersonList p

LEFT

JOIN cteDays d ON p.name = d.name

GROUP BY p.name;