I actually did it once, about 2 years ago before I had a residency, I was on the 10th month of overstay (October), and was inquiring about residency process, somehow a person at IMM suggested I pay an extension, I paid 1,000 pesos and my extension was valid for 3 more months, got a pink slip and was told to hand it over at the airport, when I left that December I did not have to pay any overstay fine at the airport, so basically by paying 1,000 pesos at IMM for an extension I avoided paying 2,500 pesos overstay fee at the airport.
Again, this was 2 years ago and things may have changed.
Again, this was 2 years ago and things may have changed.