If you are flying out of Chile at SCL, the PDI/International Police have an office there (the area where you line up for outgoing passport control) to pay the overstay fine (can someone confirm?).
If leaving Chile elsewhere, you will have to pay the fine first at the nearest Extranjería office.
At SCL, you could try to see if they let you pass but prepare to pay the fine after they make you feel like you committed a capital offense.
Just a SPAM KILLER. You are on your own in this forum. My personal mission here is done.