The thing the surprises me is that from a legal perspective, (NAL) it sounds like it makes sense not to host the LLMs. Merely to license them to others. Then it becomes a dual use tool like any other and their culpability drops.
For example, the huggingface hack is absolutely OpenAIs responsibility and they should be sued to the hilt. But if someone else uses a self or third party hosted anthropic model, they can escape liability (mostly?)
Same as with the argument over trucks, knives, and any other dual use item is used as weapons. you don’t blame the manufacturer.
(I am merely pontificating here. The law and precedent is nowhere near caught up on this)
Not hosting a defectively designed product doesn't obviate the liability of selling a product that is defectively designed. The liability is for designing and selling a dangerous product, not for hosting it.
To the extent they are representing that Claude is potentially sentient, there could be some VERY interesting principal-agent theories (agent in the traditional legal sense) that need to be ironed out to determine liability. It would not shock me to see someone forced to answer on the record as to whether Claude is an autonomous individual for legal purposes in the next couple of years. If they represent that it is, they'll have to explain the scope of its authority and such.
The answer to this question represents the difference between throwing a hammer at someone - the hammer is essentially just an extension of your body - and paying a hitman to brutalize someone. In the first case, you're only on the hook for assault or battery; in the latter case, you're potentially on the hook for conspiracy, solicitation, etc.
And then there is of course the question as to whether Claude is the agent of the user prompting it or of Anthropic itself. But, as you say, this is a wide-open legal question.