Years ago I was in Brazil and my 90 day visa was due to expire soon.
The family that had befriended me said "You must go see our cousins in Londrina. They can help you."
So I went to Londrina. The cousins drove me to the border with Paraguay. There I was told to "Stay in the car, say nothing, and give me your passport." They went in to the guardhouse with my passport and came out in 5 minutes with it stamped for another 90 days.

I've always suspected that they bribed the border guard.
Have you?