Buying a used car from another state and worried about the lemon story.?

So, I am about to buy a used 2002 Mercedes from a dealer in Illinois. I live in Virginia. The car has about 60k miles on it.
I am worried that once I buy, it may not last long and break with in a month or so.
If this happens and is a serious breakdown e.g. engine or electronics etc, what can i do?

Isn't there a some kind of an automatic warranty. Apparently the lemon law does not apply for used cars.
Sometimes dealers offer extended warranty but the car is quite old and I don't think I can get extended warranty. What should I do?