First of all, read the rules and procedures of your program carefully from start to finish. Don't make major life decisions over what you heard secondhand. For one thing, as others here, I am skeptical that you would leave empty-handed. Traditionally, failing a PhD means you get a Master's as a consolation prize and shown the door. Also note that you have rights beyond your department's decisions. They might want for their department to be special but it is generally not completely within their power to make up their own rules.
Second of all, if you do want to finish, it sounds like you are in good shape. "Borderline" is a positive answer to me, you have one foot in the winning side. You did produce papers, they just weren't accepted yet. Resubmit elsewhere. That count as publications "in process". Ask your committee what additional analysis will make your thesis passable. If you fail the defense, you can redo it after improvements. If you are not up against a hard graduation deadline you can continue trying. Remember research is a field that sometimes (often actually) required dogged tenacity.
Finally to actually answer your question, in industry they want to know your skills and accomplishments apart from the school graduation requirements (about which they care little). Without even a Master's you presumably aren't looking for research jobs. So they probably expect no more than a short resume (the rule of thumb used to be one page per ten years experience) which would devote a couple bullets tops to what you did in your years at school. E.g., used method A to address problem B.
As for interviews and generally framing things, you can tell them pretty much anything. Google around and you should find many good ideas. The critical thing is to be positive and avoid the appearance of being a quitter. For example, you decided research wasn't for you and you wanted to do "real work" (particularly the kind of work they do at the place who asked you the question). Or even just that you couldn't take being a starving student anymore. Or you didn't want to overspecialize your career in research. It's pretty easy to convince people who also didn't want a PhD, that you had a good reason for not wanting one yourself. This isn't really a question to ask academics, but industry professionals instead. Note that these answers are actually not lies, since you could have continued to work towards a doctorate if you really wanted to but are apparently deciding not to.