Should I expect to be paid for post-graduation research?
You should ask the professor. However, in my experience, the default assumption is that you will be not paid (if not said otherwise). It is often hard (again, in my experience) for professors to obtain funds for short-term-positions.

Note, however, that you are under no obligation to finish the project without getting paid. So before working on this for free, think about if you have time for it and would profit from it in some way (e.g. if you like thinking about it or if a publication is good for your life/career).

So to make clear the answer to the question: Ask, but do not expect.