Pre-Employment Candidate Screening

Situation: I was contacted by a former employer ( large organization) for an open career opportunity. I am currently going through the interview process but this employer let me go about 8 years ago for substance abuse issues. I know I signed a document but unsure if it included a right to not rehire. My concern is that if for some reason this does not come up in the screening process can they fire me post offer. Questions: Will this definately come up in the screening process? Can they exclude me from rehire if nothing was indicated in the exit process about right to not rehire? Can they fire me if this comes after being hired?