What exactly does termination from a PhD program entail?

This is normal practice these days at universities. In the old days, doctoral students could drift away from their program mid-stream and people wouldn't really care. They might return after 20 years to submit their dissertation, but otherwise there was no attempt to track these zombie students down.

Unfortunately, many places are now using average time-to-degree (TTD) as metrics to a graduate program's quality (purportedly a lower TTD is better). Zombie students are problematic as you can have someone who is 15 years into a program without graduating, dragging the average up. Note that there is a difference between a nominal TTD and actual TTDs -- for example, in my old university the nominal TTD was 5 years but very few people actually graduated in that time, the average was closer to 6.5 years.

In my experience, provosts are asking departments to track the zombies down and determine whether they should be terminated or not. Being terminated isn't a bad thing, it means that you will be left with your last degree (e.g., M.Phil) and you shouldn't really call yourself ABD as you won't be permitted to submit. I've been through a few of these cullings and as faculty I think they are a good thing as zombie students on the books really help no one.

If you have any hope of submitting, I would ask that you be given some time (1 year would be reasonable) to submit. Otherwise, I would take your MA/M.Phil and be happy with it. I don't think there are any negatives for a career in industry. Again, you technically shouldn't call yourself ABD (rather you "withdrew from program after meeting all qualifications for the doctorate but the dissertation") but I really don't think anyone is going to check. Think of it as a general discharge, under honorable conditions.

Regarding background checks: at a US university, your educational records should be protected by FERPA and nobody should be able to access them without your permission.

However, you should probably assume that a potential employer would be able to learn the following things: You used to be enrolled in the PhD program, you're not enrolled now, and you didn't receive the degree. (Some of this would be "directory information" which FERPA does not protect; other parts might be otherwise publicly available, such as from old department web page listings of grad students.) So they can reasonably deduce that you either quit voluntarily or were kicked out ("terminated").

Some employers might also require, as part of the job application process, that you give them a copy of your official transcript from the university. If you are terminated from the program, the transcript will state this, and probably explain the reason ("didn't complete program requirements within time limit", "didn't make satisfactory progress", something like that).

If you don't think you will be able (or willing) to either defend before the deadline or negotiate more time, you might see about voluntarily withdrawing from the program. ("You can't fire me, I quit.") This might not look as bad on a transcript. After all, it's not uncommon for people to start graduate programs and then decide it isn't something they want to pursue, and you could explain it to an employer in those terms. ("I decided that instead of academic research, I wanted to work in industry, so that I could do work that was more practical / real-life / lucrative.")