Upon admission, you are provided with an I-20 that is then presented to a Consular Official at the US Embassy in your home country with your request for an F1 Student VISA. If approved, your passport will have a student visa permanently affixed with a start and end date. If you are in the United States beyond the end date but still "in status", you will not have a significant problem IN the US. However, once you travel outside of the US, you may not be allowed re-entry.
Response is applicable to the Miami Campus only.