typically, when overstaying a visa a passport is stamped on exit, and re-entry into brazil can result in a fine, can be denied, or both - so it is important never to overstay a visa.

travelers wishing to transform their visit in brazil into a legitimate permanent stay, can do so by applying for the proper visa - depending on the individual's status, there are paths to getting work permits and work visas, as well as student visas for those who decide to study in brazil. 

there are several agencies that can help obtaining the visas - very conveniently, these agencies follow the entire process via mail, and allow getting visas without having to travel to a city where the Brazilian consulate is located.