I think the answer is "they won't."

Mrsmicah got a "see agent" message this morning when she tried to use her Easypay card that she's been drawing down for the last couple weeks. I just checked her ride history and she started Friday with a $2.95 balance. She swiped four times Friday evening (she and a kid taking a roundtrip) and managed to get in one more swipe on Saturday afternoon before the Friday swipes posted. So her end balance was -$8.65 and the card is now in "revoke" status (just like it used to do if you fell below $20 and didn't have a valid credit card in the profile).

I suppose it's possible the AirTrain turnstiles communicate with the Easypay computers in more real-ish time than the NYCT turnstiles. But it seems unlikely. We do have one more easypay card with a few dollars on it and need to drop off a kid at JFK in a couple weeks, so maybe we'll find out.