I don't think the publishers will be liable here.
They have been misled by the author.
The reality is that with life writing/memoir, it's a subjective account of someone's version of their reality and so 'fact-checking' and 'due-diligence' don't really apply. You can't as a publisher ask for someone's medical records, for example. You have to take people's word for it, and so that does make this genre quite open to being taken advantage of by shysters looking to tell a hard luck story.
I'm fine with some artistic licence and embellishment - shaping anyone's life into a 'narrative' for public consumption is going to take some of that, after all - but when the central feature of a memoir is about overcoming the odds of a terminal illness when that terminal illness doesn't exist - then you're on very dodgy ground.
Penguin Random House will probably stop any further reprints of the existing books, and they will have to add a disclaimer to any future editions should there be any.
I would imagine they will either cancel or indefinitely delay the upcoming book altogether as sales will not be good - the public will have lost confidence in the author, and if the content of the book centres around Moth's illness - which I believe it does - and this is under question, they won't want to risk the potential blowback if it does come out that he never had the diagnosis at all.
This is going to be a big financial hit for Penguin, but they are insured against this kind of thing. Raynor Winn won't be, so I hope she's saved the money she's made, as she won't be making much more for the foreseeable.
I feel sorry for the people involved in making the film - a deal is apparently pending for the film to be shown in the US and wider European markets, but with all this furore, I can't see this going ahead now and they will be limited to their takings made in the UK. It'll be difficult for them to make a profit now.