This kind of interview can take many forms, including having two interviewers adopt a “good cop, bad cop” routine; asking bizarre questions out the blue; or leading you into perilous territory, by asking, for example, what you would change if you were boss of the company.
Remember that most of these scenarios are meant to test your ability to react to the unexpected. Remain calm and give a rational argument to support any point you make — in this kind of interview, there are often no correct or incorrect answers. Above all, just don’t become flustered.
One of the thorniest issues that can arise in an interview is that of a departure from a previous job. If you were fired, you will probably have to say so — the likelihood is that any prospective employer will find this out via references even if you deny it.
But don’t just say you were fired and leave it at that. You might, for example, say that the job description turned out to be very different from what you had been led to believe. Or you could always blame health issues that have now been resolved. In short, be sure of offer some constructive explanation, but avoid smearing your previous employer.