Can a foreign key also be used as the primary key in the same table?

For example:

create table Table1
( T1_Id    integer     not null primary key
, T1_Data  varchar(9)  not null
)
create table Table2
( T2_Id    integer     not null primary key
, T2_Data  varchar(37) not null
, foreign key (T2_Id) references Table1 (T1_Id)
)

Why would someone design two tables like this? If it's a one-to-one relationship, couldn't you just include T2_Data in Table1? Yes, you could, although then you would also need to allow T2_Data to be NULL, if not every T1_Id has a matching T2_Id—in this case it's actually a one-to-zero-or-one relationship.

If it's a true one-to-one relationship, where every T1_Id has a matching T2_Id, then you could combine them without NULLs. Then the only reason why you might want separate tables would be if T2_Data were (a) infrequently queried, and (b) so large that it would result in many fewer physical rows on a physical database page, which would imply poorer performance for queries that used only T1_Data.