on the 38xx series, you could get a percentage via the printer LCD panel through the status menu.
the printer will stop when the cartridge finally runs out and then re-start (picking up where it left off) when a new cart goes in.
the 'low ink' warning is really seen as 'order a new cart now' warning. Just keep printing but have spares on-hand.
I've got an LC cart that has been flashing low ink for a while now and the printer says '2%' left. I probably just jinxed myself.
Be aware that doing things like nozzle checks and maybe even a black swap will freeze the printer as it insists on having more ink. you can always put the low cart back into the printer after.