Is it possible to get an STD from someone who does not have an std?

No... …you cannot catch a disease from someone who doesn't have the disease. There are people who are asymptomatic carriers of disease - meaning they have the disease but have no symptoms and my not know that they can transmit it, always have protected intercourse.
No. No, you can't get infected with what is not there. But, how are you so sure that they didn't have one?