A special counting / calendar table is created in cte0 and cte1. Once we get this, little needs to be calculated and grouped around the island.
The counter currently has a maximum of 10,000 days (27 years), but you can easily expand the tilling table by adding , cte0 N5
;with cte0(N) as (Select 1 From (Values(1),(1),(1),(1),(1),(1),(1),(1),(1),(1)) N(N))
,cte1(R,D) as (Select Row_Number() over (Order By (Select Null))
,DateAdd(DD,-1+Row_Number() over (Order By (Select Null)),(Select MinDate=min(EffectiveDate) From
From cte0 N1, cte0 N2, cte0 N3, cte0 N4)
Select MemID
,EffectiveDate
,TermDate
,SinceFrom = Min(EffectiveDate) over (Partition By Island)
,Tildate = Max(TermDate) over (Partition By Island)
From (
Select *,Island = R - Row_Number() over (Partition By MemID Order by TermDate)
From
Join cte1 B on D Between EffectiveDate and TermDate
) A
Group By MemID,Island,EffectiveDate,TermDate
Order By 1,2
Returns
MemID EffectiveDate TermDate SinceFrom Tildate
123 2016-12-03 2017-01-10 2016-12-03 2017-03-05
123 2017-01-11 2017-02-06 2016-12-03 2017-03-05
123 2017-02-07 2017-03-05 2016-12-03 2017-03-05
123 2017-03-08 2017-04-15 2017-03-08 2017-05-24
123 2017-04-16 2017-05-24 2017-03-08 2017-05-24
Edit - now if you need a compressed data set
Select MemID
,EffectiveDate = Min(EffectiveDate)
,TermDate = Max(TermDate)
From (
Select *,Island = R - Row_Number() over (Partition By MemID Order by TermDate)
From
Join cte1 B on D Between EffectiveDate and TermDate
) A
Group By MemID,Island
Order By 1,2
Returns
MemID EffectiveDate TermDate
123 2016-12-03 2017-03-05
123 2017-03-08 2017-05-24