The scenario is really this simple, "there's really no way even to offer a solution until you've determined liability", duh!
In reality, that is not true. If you can find a resolution that all parties willingly accept, you have a solution. If all parties find the solution acceptable but you have not officially declared who was at fault, that's OK unless somebody insists for their personal satisfaction that you say who was at fault.
Which is the case I constructed.
In the particular case you describe that looks unlikely. The LOL cannot be made whole, literally, unless she gets more money than the coop has.
EXACTLY! That is why I created the dilemma. Does equity demand that LOL be made whole at the expense of innocent parties, no matter how bad off this leaves her and no matter how deep are their pockets?
So you designed a case where the owners are innocent, and the coop looks innocent, and the LOL is innocent, but Bobby is negligent.
And you want us to agree that the innocent owners should not have to pay. I agree with that. I agree with that even without a limited liability sign.
What about the case where the owners are guilty? Should limited liability also get the owners off scot free then?
Really, this is about theft. These farmers are in the Co-op business to make money. They make money by providing goods at prices people find reasonable. This benefits everyone, including LOL who buys her cat litter there rather than from the door-to-door cat litter man. The Co-op is a buck cheaper, but they limit their liability.
And the coop's net worth is $1 million. Add up the savings everybody gets by dealing with them versus dealing with competitors. Does it come to $2 million? It's possible that they have not in fact done more good than harm. But the good is spread out over all their customers, and the harm is just to this one LOL who was going to die soon anyway because she didn't have enough money for rejuvenation treatment.
Maybe they really ought to close down.
So if the LOL choses to assume the risk to get a buck off at the Co-op and some individual's negligence causes her damage, is it okay to steal someone else's money to make her "whole" (while, by definition, making the richer person who did her no harm, less whole)? Remember, damnum absque injuria.
When the farmers are innocent, I think it's not right to take their money. As near as they could tell the coop was being run carefully and correctly by responsible people.
To the extent that the coop was in fact being run carefully and correctly, it's not right to take their money either.
So then there's Bobby. he has $1000 and a strong young body. If the medical industry will pay, say, $2 million for all his fine young organs, he could pay his debt. Would that be appropriate? The death penalty for a simple mistake? It might be. It depends on how the customs go. (Note some of Larry Niven's stories about thumb-runners etc.)
But if employees automatically accept all liability, won't they demand higher wages? I guess they'd want to, but it would depend on supply-and-demand. If your choice is to starve or else take the job with a possible automatic death penalty if you make a small mistake, you take the job.
But wait! How about the store puts up a sign that says they have a maximum $500 limit for any damages paid. Or even $50! Then no matter what happens you can't collect more than $50 from the coop or its employees! Bobby can never have to pay more than $50, and he's home free just like the owners and the coop! Problem solved!
You are not interested in solving the particular problem but in establishing a precedent. So you probably want the extreme case.
If I am poor or if I am rich, I want the vindication of establishing that someone was liable by sticking it to them. You think this is extreme? My friend, it happens all the time, in every sort of situation, in current judicial systems.
It often does, but it does not have to. And when it does not happen then it is possible to reach a settlement without a declaration of liability. In fact, doesn't that often happen IRL? The parties reach a settlement out of court, with no admission of wrong-doing by anybody? Sometimes after a court case has progressed pretty far.
LOL's wealth is irrelevant to liability. She and the other parties have agreed to arbitration. After the determination of liability phase of the hearing would come the assessment of damages phase, but these to phases must occur in this logical order.
If the parties demand that, then that's how it has to be. But in general it does not have to be that way and determination of liability does not have to happen first, and facts of all sorts can be collected in any order.