Associate adjunct professor to Assistant adjunct professor in USA Is it possible that an Associate adjunct professor becomes  assistant adjunct professor in USA university within same department of that university?
This is likely much more common than for non-adjuncts. The protections for adjuncts are pretty weak generally. However, there are situations in which adjuncts are unionized and then the union rules would apply. 

Also, the typical adjunct position is a fixed term contract that might be renewed or not. The nominal rank would be part of the contract. 

But possible? Certainly. Not common, though.