Playing a sound when turning off a circuit
There is definitely a power source needed in place of mp3 player side. You should consider using a supercapacitor which provides enough power to play the music. Since you're using Arduino consider two power sources, one from 7.2V battery (primary) and another from 5V super capacitor (secondary). Take inputs from 7.2V power sources to ADC pin and programmatically check when the primary power is going off. When primary power goes off, enable secondary power as well as trigger the music part which may be connected to a digital pin.
PS: You need to make an circuit for managing two power sources using MOSFET which is similar to how Arduino UNO manages USB and External DC jack power supply. Check reference schematic for that.