They should just call it what it is: unplanned deco!So, do you think that "emergency deco" is a good term? I wonder if any other agency uses that?
Even as a newbie, I remember enough about NDL from tables for the expected max depth (or check tables I carry) to have a good sense of min NDL before I start the dive. Once I get to depths where NDL would start being a concern, I check my PDC regularly to ensure I've started ascending by the time my NDL hits 5 minutes. I agree that, as long as you are paying attention, you should never get to this "accidental" deco.
However, I've already seen divers do exactly that though - last trip it was a guy who was too busy chasing critters with his camera and ignored the DM's signals to ascend. Luckily he had enough air (and the boat had regs hanging at 20 feet just in case). The DM had some choice words for him topside and he was not allowed to do the second dive (and, believe it or not, he was annoyed).