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As of my experience the "part" that would most likely break
1. Integrity between UI and the middleware.
2. Integrity between middleware and DB.

The area which most likely to break is Middle-ware Layer which actually has business logic for the Enterprise Software Application. Middle Layer is also known as controller logic as it communicates between upper layer (GUI) and lower layer which is Database.
The other reason this layer is likely to break because most complex algorithm and computations takes place in middle layer, also this layer interacts with lower and upper layers.
So good testing strategy would be do functional testing for the entire feature which is implemented so middle layer gets tested.

The area that is most likely to break (according to me) is GUI part, because we have an application with structured architect with front end that we can use.
GUI
^
DATA_PROCESSING
^
DATABASE

If we have any issue with database the end result we expected will be wrong.
If we have any issue with data processor then again end result will be wrong.
And if GUI has any issue we will be able to see it.
So in any case end result will be wrong(in front end). So our emphasis should be on to break GUI, as after this we can easily debug to the lower layer.

I would break it into MVC model which is MODEL-VIEW-Controller as follows:
View: Handles all work related to UI.
Model: Where all logic will be made
Controller: The which routes the user request from View to Respective Model and sends the response back to Respective View.