Nozick actually asks at what point did you cease to be slave, if ever. The question assumes that you start in slavery. Aristotle would define this as "circular logic".

I have always been a fan of the Ancient Greeks in these types of logical arguments. Socrates would ask you to, "Define your terms" before either agreeing or disagreeing with a premise. In this case the question is, "How do you define slavery?" Once I know how you define it, I can begin to discuss at what point you cease to be one.

"Freedom", now that's another enormous concept. "At what point is a slave free?"
Tell what you define as freedom and I would say he is free (according to your definition), when his condition satisfies your terms.