I'm using a Li-Ion 7.2v camera battery as a power source for some of my random Arduino things sitting around.
For some reason, I'm thinking it's bad on a li-ion battery to be drained all the way to zero. Is this true? And, will Arduino keep drawing power if the voltage becomes too low?
Yes, and yes. You need UVLO (undervoltage lockout) somewhere along the line. It may be that the battery's protection circuitry has UVLO functionality built in - this is sometimes done.
Yes it will. Even the MKR1000 and MKRZero which have a dedicated LiPo socket and charging circuit doesn't shut down when the cell volts goes below 3V!!
So, what do you do about that? Do you go through the effort to build out the UVLO circuit? It seems like this would be a handy thing to mass produce in some sort of IC package. I see a few things on Digikey but haven't looked super hard yet.