You don't have to eat the cost of the overlap, and they don't send you a new metrocard, they credit the credit card you used to purchase the metrocard. You never stopped getting unlimited metrocards, but you are credited for the overlap. E.g. your $100 card gets borked on the 15th of the month, you buy a new card on the 15th, through the next 14th, and you get $50 credit for the 15th through 30th. You've essentially sold 1/2 of your original unlimited back to the MTA and changed the date of your cycle.