SQL Server 2019

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Create Table Emps(person VARCHAR(50), started DATE, stopped DATE);

Insert Into Emps Values
('p1','2015-10-10','2016-10-10'),
('p1','2016-10-11','2017-10-11'),
('p1','2017-10-12','2018-10-13'),
('p2','2019-11-13','2019-11-13'),
('p2','2019-11-14','2020-10-14'),
('p3','2020-07-15','2021-08-15'),
('p3','2021-08-16','2022-08-16');
7 rows affected

With CTE as 
(
 Select D.person, D.started, T.stopped, 
       case
         when Year(D.started) = Year(T.stopped) and D.started > T.stopped 
           then 1 
           else 0 
       end as chk
 From
 (Select person, started From Emps Where started >= '2016-01-01') D
 Join
 (Select person, stopped From Emps Where stopped <= '2017-01-01') T
 On D.person = T.person
)

Select Count(Distinct person) as CNT
From CTE
Where chk = 1;


CNT


1


With CTE as 
(
 Select D.person, D.started, T.stopped, 
       case
         when Year(D.started) = Year(T.stopped) and D.started > T.stopped 
           then 1 
           else 0 
       end as chk
 From
 (Select person, started From Emps Where started >= '2016-01-01') D
 Join
 (Select person, stopped From Emps Where stopped <= '2017-01-01') T
 On D.person = T.person
)
Select person, started, stopped
From CTE
Where chk = 1;


person
started
stopped


p1
2016-10-11
2016-10-10