There's a lot of assumptions about how society is organized buried in your questions that are worth unpacking, and let me say up front that I don't think you're going to get a single, straightforward answer.
First, you are implying the continued existence of civil and criminal law, more or less as it currently is. Personally, I think both of those are bad systems independently, and even worse and more absurd when combined.
Second, you almost seem to imply a socialist world to be a sort of market-based cooperative system? Many of us dream of a more radical world. Though specifics vary, usually we hope that our new economic system will be based on collaboration and comradery, not competition and profit. Theories on how that social collaboration should happen vary widely, but any in case, many of us dream of a world without money, in which case the assumption of pecuniary damages breaks down.
You say you're not a socialist, and the world without money causes eyerolls among many non-socialists -- it is such a ridiculous pipe dream, no? How wildly unrealistic! We socialists have many ways of talking about this eyeroll-inducing phenomenon. Mark Fisher called it "Capitalist Realism," famously saying, in his book of the same name, that "it is easier to imagine the end of the world than it is to imagine the end of capitalism."
This force is so powerful that we cannot even imagine a world without a modern conception of money, yet we know they have existed for all of human history, including in much more recent times and in more familiar cultures than most people realize. In "Debt: The First 5,000 Years," David Graeber gives an account of how societies have organized accounting for and rewarding labor and value, how market emerge, the much shorter history of coinage than most people imagine (did you know Homer's Greece didn't have coins?), and how societies operated with different or entirely without conceptions of money. There are even well-documented examples of societies in Tudor England functioning without money (or with so little money as to be basically without it) because of international economic factors causing metal coinage shortages.
So, to get back to your question: I don't know the details, but I do know that whatever system we'd make for dealing with (to use your example) faulty airbags should be one based on preventing the mistake from happening again. The current system hopes to incentivize companies to avoid making that mistake, and then (supposedly, though we know how it often actually works out) punishes them for making it.
I hope that, first of all, by removing profit motive, we have fewer situations like that. I don't cut corners when I work on my garden, because that's not why I garden. I do cut corners while I'm at work, as does everyone, because I work for a wage, and I usually don't really give a fuck about my employers, most of which are making shit no one actually needs (all while actively contributing to the destruction of our planet).
When catastrophic mistakes do happen, then we should focus on collaborative efforts to avoid them from happening again, not on adversarial judicial processes (that companies can often buy their way out of) that only force companies to pay "damages," often far less than the profits they made by cutting the corner in the first place. If "firms" are no longer in competition with each other, perhaps that is best done by reorganizing them, or by having outside experts from another firm conduct an investigation and give a plan, overseen by whatever body is coordinating car manufacturing (workers' councils, the state, whatever your vision is).
Think about it like this, though it's an admittedly imperfect analogy: what happens inside an existing company when one team messes up? Sometimes, if specific people are at fault, they're fired (and there the analogy breaks down a little), but in healthy companies, much more often, there is a focus on avoiding the problem from happening again. How that happens can vary.
Finally, on repaying victims' families: I want to live in a world that is "from each according to their ability, to each according to their needs." Victims and their families should not be forced to rely on the judgement of a farcical legal system to be taken care of, oftentimes several years after the event, during which they are completely screwed.
I hope that's helpful? Sorry for the tome. You caught me on a day I really want to avoid working.