Well, the experts say that there is no reason for an employee not to be able to get an interview just for being wrongly terminated. Generally, in an interview references aren't usually checked unless you are close enough to job offer. But, to see the other side of this, it might be possibly used as an excuse to slower your pace while hunting jobs. You might even fear about what the potential employer would think if he found out about the termination. In either ways, you would need to have a clear strategy in your head and get set to find the perfect job.
If people think about clearing the air by telling the potential employers about the pervious bad experiences and wrongful termination, it would really be kind of funny. You might think this to turn into 'clearing the air' stuff, but this actually would turn out into something more drastic - like a guilty confession. This is all set to turn the potential employer off. In this the employer will start taking it negatively and you will end up sounding like the bad guy. Hence, you must take it light and not try to harm yourself. There is absolutely no need to explain something you never want to bring up.
Well, you must consider yourself the lucky one. You got fired, and your previous company doesn't exist anymore. This means that the potential employer would have to try hard to track your records. In this case, you just need to reach a former colleague from our previous company, explain your predicament to him ask him if he can be used as a reference.
Meanwhile try focusing your efforts to impress the potential employer during the interview process. Prepare your best for the interview and work on professional appearance. Quite a lot of hiring decisions are made examining the chemistry between the employer and the interviewee.