What do universities usually do with a student's graded final exams?
Speaking as a professor, I typically hold on to them for a year or so just in case any student wishes to see them. That said, I can remember this happening only once in about 5000 students taught.  

When I was in college, we had the option of providing self-addressed stamped envelopes in which our final exams could be returned to us. Over half of the students availed themselves of this option.

I do not believe that my university has any formal policy, though they could have one that I am unaware of. It would seem foolish for a professor to get rid of the exams before the students have had an opportunity to see their grades and respond if something seems out of line.