That's the trick - it is not test only code. You use the same objects, the same code.

The code has to be written so it takes in the altered unit via parameters or other DI or so it knows that the current system is set to short circuit some calls.

Ie, you could have MyClient(testHTTPClient).GetResource(foo) used in tests and MyClient(realHTTPClient).GetResource(foo). The testHTTPClient would get to the actual connection part and return a configured response or error.

Your entire logic is the same, your code could "receive" a forced 404 or timeout or 200 OK. It is up to the testHTTPClient that is only changing how the http connection is handled.

I call these unit-integration tests. You are checking all units work together while not actually working with the outside world.