I believe his successor could take over the case. From the Federal Rules of Civil Procedure, rule 32:
(8) Deposition Taken in an Earlier Action. A deposition lawfully taken and, if required, filed in any federal- or state-court action may be used in a later action involving the same subject matter between the same parties, or their representatives or successors in interest, to the same extent as if taken in the later action. A deposition previously taken may also be used as allowed by the Federal Rules of Evidence.
(https://www.law.cornell.edu/rules/frcp/rule_32)
More specifically, his case was against Boeing for allegedly retaliating against him for being a whistleblower. He was a quality control manager.
So the FAA is crawling up Boeing's ass about poor quality control and lacking a safe and responsible culture, meanwhile a _former quality control manager_ is testifying about how they tried to tell Boeing about systemic quality issues and were retaliated against.
You really don't think Boeing has a vested interested in not being found liable for retaliating against quality control whistleblowers, _while being investigated for having quality control so poor people nearly died_?
If they lose this case, the FAA is going to notice, and they're going to be pissed. It's one thing to be negligent, Boeing could probably paper over that with the FAA and some small regulatory changes because they're defense contractor and vital to national security. It is another thing entirely to not only be aware of the problems due to whistleblowers but to both ignore the issues and attempt to silence the whistleblowers.
We're talking about a clusterfuck of proportions most of us can only have nightmares about. Boeing would spend the next 50 years with the FAA's hand jammed so far up their ass Kermit would feel bad for them. I wouldn't be surprised to see the SEC filing indictments for securities fraud for not disclosing known, material defects in their planes.
Even worse than that, Boeing really only has its "national security" shield in the US. I would expect Asian and especially European (because Airbus) regulators to take an exceptionally dim view of Boeing losing this lawsuit.
It's also very bad news for Boeing on any other wrongful death or injury lawsuits against them if there's a court case setting precedent that at best, Boeing retaliates against their whistleblowers, and at worst ignores them and retaliates against them. Other civil cases would be able to use the judgement against Boeing as evidence that they concretely retaliate against whistleblowers, and Boeing would be unable to challenge that assertion (you can't re-litigate the outcome of case A in case B, whatever was decided in case A is treated as fact).
Having a judgement against Boeing for retaliating against whistleblowers sounds like a great start to a wrongful injury/death claim based on negligence for anyone that got hurt on a Boeing plane. Boeing wouldn't be able to challenge that they retaliated against whistleblowers, so they would either have to claim that retaliating against whistleblowers isn't negligent (good luck with that) or that their negligence in retaliating did not contribute to that accident (again, good luck).
The importance of this case is almost entirely in second-order effects. I doubt Boeing cares about paying out a couple hundred thousand to Barnett for retaliating, they care about getting regulators off their backs and not losing every civil case filed against them for the next decade.