International students can stay in Switzerland for the time specified on their residence permit to study. It is against the law for one to stay in the country over the permitted time period. Applications for extensions can be submitted at the local immigration office.
If after completing your studies at SBS you are looking to work/live in Switzerland long-term you need to consult with the local immigration office on the process of getting a residence permit and work permit. Your future employer should facilitate you in this. SBS only provides assistance with getting residence permit to study for admitted students.