Can Tourist visa be issued in Beijing, China

Hi,
My wife has a Chinese study type which will expire in 2 weeks from now (expires 13 feb. 2015). unfortunately we have to leave china on 09 Feb. until after Chinese new year & that time of our return her X type will be already expired.
Furthermore we can not extend it as they need 21 days to do so. Now question is, can we apply for tourist type for her while we still in china?
Bear in mind that when we enter china again then she has to apply for the X type again.