Thank you for your question. The example that you give, “I am not staying,” is not a double negative; it is simply an alternate way of conveying the information “I am going.” Your second example, “I am not unregistered,” is also an alternate way of expressing that you are, in fact, registered. You will find this style often in classic novels from previous centuries. An example in my own words would be: “He was not unhappy that he had to prolong his stay.” Obviously, the meaning is that he was happy. It is simply stylistic.
On the other hand, a true double negative is incorrect English: “I didn’t do nothing.” As my teachers drilled into me in school, if you are saying that you “didn’t do nothing,” then you did do something. The correct way to express this is: “I didn’t do anything.”
I hope this helps.