The BOD (brown-out detector) voltage can be reprogrammed via the ICSP header. I think the default
value is rather low for 5V operation as its compatible with 3.3V too.
Once the supply drops below the BOD level the chip simply drops cleanly into reset mode I believe,
finessing issues with low supply voltage.
Another approach is to add a dummy load to the power supply, like an automotive indicator bulb,
which will discharges its capacitors much faster.