Technically, another person may purchase creative content, but no rights or copyrights are necessarily transferred unless specifically agreed upon by the artisan.
Creative content by one person never becomes the property of another in terms of who created it. From the moment an individual creates something they are expressing something deeply personal and in many ways cumulative of many years of development, successes and failures. By default creative content is automatically under copyright of the creator (certainly here in Canada).
Even if you purchase an original painting that does not therefore mean you have the right to create and sell prints of it. Same goes for any creative content.