Application 1 has unique records.
Application 2 needs to access a table in Application 1 but cannot change the table structures.
Application 2 may have its own table that is linked, 1 to 1, to Application 1.
Think about it for a moment. If you have a POS system that lacks customer tracking, you may have a "Customer" file in the POS system that lacks a LOT of details you need. You DO need to see your current customers though, but if you can't change the POS system, you may set up a 1 to 1 relationship between your customer tracking and the "Customer" table in the POS.
Many 1 to 1 relationship evolve from these kinds of situations. I wouldn't call them a "Case study", more of a "Were stuck doing it this way".