Why would I write a fake class and unit test it?

Don't test the mock class. Do test the production class using the mock class.

The whole point of the test support class is to have something that you can predict its behavior. If you need to test the test support class in order to predict its behavior, there is a problem.

In the fake database article you linked in a comment, the author needs to unit test his fake database because it is his product (at least in the context of the article).

Edit: updated terms to be more consistent.

• Mock - created by mocking framework
• Fake - created manually, might actually function some.
• Test Support - Mocks, Fakes, Stubs, and all the rest. Not production.

You are not testing your mock object but some other class that is interacting with it. So you could for example test that a controller forwards a save method call to your fake repository. There is something wrong if you are "testing your fake objects"