It's entirely possible that something happened, unrelated to your performance as a pilot, that led to a termination or something along those lines. Bosses daughter, someone didn't like your politics, whatever. I've seen it happen. In such a case, historically, the best bet is to put distance (years) down the road and leave it behind. Up until PRD, anyway. Whereas PRIA was a request process (requirement) going back a few years, PRD is a permanent record, in one clearinghouse. It has the disadvantage of not being able to outrun your past, but the advantage of foresight: you'll know what's there and you can address it.
The light in which you're viewed regarding your past is two-fold: it's about the events that are recorded and reported, but it's also about how you deal with them and present them (attitude, altitude, and all that). The ancient, sage advice to come clean, own your past, and show what you've learned from it can be a strong point in your favor, but you have to be in front of it to do that. You have to own it outright and explain how, why, and where it's got you today. If it's something you hide and only admit after being confronted, then it becomes a problem.
Life is full of gray areas. You worked for a union, the company came after you. Negotiations were in play, and any shots across the bow were the company's way of putting pressure on the union. You made a minor screw up, company fired you. You filed a grievance through the union, and it was settled with back pay and the company agreed to accept a letter of resignation, converting it from a termination to you quitting. Fair enough. You don't want to work for them after they did that to you, anyway. You move on. You're happier, blood pressure goes down. You don't look back. But, your next employer does.
So, here's a gray area. The separation from the company was a firing: it was a termination. Your former employer, as part of a legal settlement, agreed to accept your resignation, six months later. They paid you back pay...pretty good exoneration; read between the lines and know the company wouldn't have paid you if you didn't have a case. They knew they were wrong. But you really can't say that, doesn't look good, no matter how you slice it ("yeah, I hit back, got paid, got a legal settlement to cover it up..."). The illusion is relatively complete: you have a legally binding agreement to convert the termination to a resignation...not that uncommon for employees to resign, quit, etc. Also a bit of a red flag, sometimes, because "resign" is often tacitly viewed as quitting under pressure...sometimes viewed as one step up from firing. That said, it's made the best of a bad situation, legally...except: the company can't lie when records are required under the law. They can't change your history in those records.
When the union was fighting the company for the new contract, and you, as their steward, walked around with a big target on your back, you became the bullseye for that shot across the bow. You made a minor mistake. The company had a policy about flap use, or something like that, and you followed it, resulting in a blown tire at a high density altitude field. The company grabbed onto it, fired you for whatever reason, but it went in the records as a violation of company policy. A memo went to the training department, give this guy remedial training, but in the meantime, before you got there, the company saw the opportunity, and fired you. The company has, buried in those training records, a memo about the real reason you're gone, so far as they're concerned. Violation of company policy, blown tire, whatever. If anyone asks the company about the reason you left, they have a legal obligation to say you resigned. HOWEVER, the records can't be altered. While your resignation letter can be inserted into your HR employment jacket, your training department file is sacred, and if it says something else, that's going to appear.
Know before you go: know what other employers are going to say about you. Review your records. Review all of them; see what former employers have submitted, see what is in your FAA and PRD records. Get a copy of your driving history, and pull your credit. An employer may have told you one thing, but may have written another. It does happen. Mistakes occur, and some have a vindictive streak, too. Some operators have little fifedoms in their operation, complete with Napoleon-complex czarist autocrafts, and who knows what might lurk? You can know, however, and that's the best way to get ahead of it. Find out what's reported. If you're unsure about how to address the past, or what to disclose, see what's been disclosed already, see what's reported to the PRD, etc. Did that legal agreement to convert your termination to a resignation play out as intended? Find out, and then know whether to report it this way, or that. Both are legitimate. Neither are a lie: if you say you were terminated, that's true. If you say you resigned, that's also true. Better to say resigned, if able, but know how to address it. Talk to an attorney, former union personnel, etc.
Looking back, you may determine that you need to explain the resignation, after you've determined that your records don't show it as a termination. It does need explaining: did you resign because you were about to be fired, or did you resign to go to another job, or were there other, extenuating circumstances that might also require explanation? Those records to have mention, as it turned out, of the incident that led to the termination/resignation, but don't say anything about termination. You still need to get ahead of it. Perhaps you can disclose the event in advance, simply say that you, and the company, didn't see eye to eye on the matter, and you determined you'd prefer to go elsewhere.
Gray areas. Some of this is best addressed with a coach; you may find that an experienced coach who does employment preparation has seen this, and every other shade of gray, before, and has helped hundreds, maybe even thousands of other pilots polish and explain history in a way that paints them in the best light. Call it spin, call it the fine art of diplomacy, call it preparation: it doesn't hurt to sit down with someone who does this for a living, and work out the best way to get ahead of anything that you might need to explain. Skeletons in the closet aren't nearly as scary in the daylight.
With PRD, ancient employers will still be in the record books, years down the line, and you can expect to have multiple employers in your career. This is aviation. If you haven't see it yet, you will...bankrupcies, mergers, furloughs, downsizing, whatever...you'll ride the roller coaster if you stick with this, and you'll ride it more than once. Why did you go fly a Cessna 210 doing night freight, when you had a cushy job in a 767? Furloughed, took what you could find until recalled? Easy explanation. But what about that period when you didn't fly for a year? Family emergency. Okay. And that time you switched jobs, went from captain to F/O, similar equipment, similar employer...looks like you resigned? Tell us about that. Helps to get ahead of it, be prepared with the answer that works in your best interest. Don't lie. Don't hide, but you have to paint with the colors you've got and you have to know what they are...get the information, and determine what, if anything, you may need to address, and how best to address it. You can approach the same incident or subject from several different directions, and leave several different impressions.
Excuses are never complimentary. Don't use them. Concealing never looks good. Lying is a cardinal sin. But outside of that, we're all human. Few careers are picture perfect. We move. We divorce. We marry. Families form, members die. We get sick. We get well. We make mistakes. We make choices. Sometimes, choices are made for us. The economy rolls on. Life happens. Know how that's reflected in your records, and how to best discuss that reflection. Given a new record-keeping and record-reporting system, that's a life-long reflection, so get ahead of it now, keep ahead of it over time, review it from time to time, and get comfortable with the way you'll address it. Whatever questions you're asked tomorrow, you'll be asked again in five years, ten years...you'll see this material again. Be comfortable discussing what needs to be discussed. History isn't just what happened. History is often known in the way it's recorded, the way it's retold, and the lens through which it is viewed. You have some control over that; empower yourself by staying informed.